Writing Tips Shortening Sentences - Proofread My Papers Blog

Composing Tips Shortening Sentences - Proofread My Papers Blog Composing Tips: Shortening Sentences Quickness is broadly the spirit of mind, however it’s additionally profoundly esteemed in the scholarly world and the business world. Why? Since composing compactly will assist you with expressing what is on your mind obviously, making your work progressively effective. Maybe the most straightforward approach to make your composing increasingly compact is to abbreviate your sentences. Conveniently, we have a couple of top tips for doing precisely that! 1. Stay away from Redundancy â€Å"Redundancy† implies utilizing extra words that don’t add anything significant to a sentence. The expression â€Å"twelve midnight,† for example, implies the very same thing as â€Å"midnight,† so the â€Å"twelve† is excess. It’s in this manner a smart thought to check your sentences for superfluous words, as removing these will make a long sentences shorter. For instance: In established truth, each and every attendant worked from 3 am in the first part of the day to twelve 12 PM. Could be effectively changed to state something very similar with less words: Truth be told, each medical attendant worked from 3 am to 12 PM. Must be the reason Florence Nightingale consistently looked so drained. 2. Separate Long Sentences Once in a while, long sentences are simpler to follow whenever separated into at least two articulations. The accompanying, for example: Making a sentence too long can be befuddling on the grounds that it is anything but difficult to forget about information disclosed toward the start, since they don't give the peruser sufficient opportunity to process what they are perusing and before the finish of the sentence you may have overlooked where it began! That’s 51 words with scarcely a respite for breath. It would bode well to separate it into three shorter sentences: Making a sentence too long can be confounding. It is anything but difficult to forget about information exchanged toward the start, since they don't give the peruser sufficient opportunity to process what they are perusing. Before the finish of the sentence you may have overlooked where it began! 3. Be careful Padding Words Cushioning words and expressions are things like â€Å"in my opinion† or â€Å"as a matter of fact,† which make a sentence longer yet don’t for the most part include a lot of importance. Saying â€Å"In my conclusion, the political environment is toxic,† for example, implies precisely equivalent to â€Å"The political air is toxic.† If you have to abbreviate a sentence, have a go at searching for cushioning phrases you could expel. 4. Utilize the Active Voice We’re frequently instructed to keep away from the dynamic voice in scholastic composition, however some of the time utilizing the detached voice makes sentences clumsy. For instance, the aloof sentence: The speculation was bolstered by the outcomes. Could be made somewhat less complex by utilizing the dynamic voice: The outcomes bolster the speculation. 5. A Final Thought†¦ Utilizing just short sentences can make your composing need familiarity. To make your work drawing in, the best activity is shift sentence length. You would then be able to spare shorter, punchier sentences for when you have to make a commanding point or guarantee clearness.

Low employee satisfaction in Air Arabia

Low worker fulfillment in Air Arabia Air Arabia was propelled in 2005 as one of the activities in ease transporters fragment in Middle East. Over the timeframe it had the option to develop an amazing organization name in the market alongside a firm monetary record of its own. In the wake of acquainting issues related with Political, Social, Environmental and Technological (PEST) parts of Air Arabia, this part focuses on breaking down these issues with the assistance of essential authoritative conduct hypotheses. The report is separated in four segments, every one for Political, Social, Environmental and Technological perspectives. In each area, OB worry of the issue followed by the issue from the case and the clarification is referenced. Individuals: Issue Statement: In past area we found an issue that representatives in Air Arabia were not happy with the low monetary advantages gave against their elite. Issue Highlight: Performance based Incentives Execution based motivations: This is an issue of pay for execution plot. In pay for execution or state execution based motivating force framework, representatives are remunerated in understanding to their exhibition. Presently the issue is that workers can never be happy with the result of this specific type of remuneration framework. This can be comprehended by Equity hypothesis. Value hypothesis expresses that workers use to think about their situation (here remunerations) with those of different representatives. So even an association stay straightforward in appropriating motivating forces, until except if the representatives themselves become fulfilled considering value hypothesis, the issue like the motivator issue in pay for execution plot in Air Arabia remain standing.â [1]â Issue Statement: One of the serious issues related with representatives is that organization can't furnish them with long haul duty in regards to their exhibition evaluation and work viability reward. Issue Highlight: Performance Appraisal Execution evaluation: Execution examination is the proportion of assessing the presentation of the workers. In air Arabia, the exhibition evaluation framework directly being used fuses the quantity of undertaking and time breaking point of those errand achieved by the workers are recordedâ [2]â . This structures the premise of the exhibition examination plot in the organization. (Execution related compensation, 2005) Now the issue in this plan is this doesn't tally the quality and circumstance under which work is done. For instance, in Air Arabia, the exhibition conspire is same for deals and managerial staff. Presently authoritative staff has clear work capacities to follow while deals staff needs to experience documented work which is all the more testing. The objectives for deals staff are harder to accomplish than those of managerial staff. In this way the exhibition evaluation conspire in Air Arabia isn't good and requires different plans like 360 degree plot etcâ [3]â . Issue Statement: The case shows that Air Arabia displays issue of workforce the executives because of workforce decent variety. Issue Highlight: Diversity Assorted variety: Pioneers and supervisors in Air Arabia don't deal with the workforce decent variety successfully. In their push to deal with the decent variety, they go with equivalent treatment system. In this methodology, every one of the representatives is dealt with similarly regardless of its cast, shading, race and language they talk. This looks very reasonable in first look yet the methodology isn't useful in nation like Dubai. The nation has individuals of various religion and cast, communicating in various dialects and has diverse instructive plans and mental aptitudeâ [4]â . Presently the issue is some specific sort of representatives are consistently beneficial of this correspondence approach. For instance, the work power of India is more conversant in English than the locals of UAE. UAE culture gives accentuation on Urdu and not English. Presently in view of low capability in English and the uniformity approach in decent variety the board, UAE locals are generally under-evaluated than hardly any remote classes of worker. This presents a feeling of disappointment and un-bliss towards the activity. Issue Statement: representatives of Lufthansa Air picketed to improve their working conditions. Issue Highlight: Work Environment Workplace: Workplace is a significant constituent of a successful hierarchical culture. The workplace not just comprises the physical constituents of the area yet in addition the way of life of the work like senior-subordinate relations, kind of correspondence etcâ [5]â . The circumstance here shows that the representatives of Lufthansa Air are not happy with the workplace and took to the streets. The real explanation behind the disappointment was company㠢㠢‚⠬㠢„â ¢s strain to work more than the necessary 8 hours to answer the expanding rivalry in avionics industry. This choice was not invited by the staff as it brought about more quickness in employment and subsequently brought about inappropriate work conditions in the organization. (Tuning in, the Doorway to Employee Commitment, 2005) Condition: Issue explanation: Air Arabia needed to decrease a portion of its different costs like HR consumption and to make it conceivable it has diminished admission of representatives that had expanded work pressure over directly working workers enormously. Issue Highlight: Work Environment and Employee Shortage Workplace and worker lack: The issue here is of terrible workplace because of over the top remaining task at hand due to lesser number of representatives. The issue was come about because of high oil costs which constrained the organization to shrivel the workforce. This shrinkage brought about high weight on present work culture and subsequently diminished effectiveness of workplace. Issue Statement: High operational cost which is inner factor of worker failing causing outside impact over association. Issue Highlight: Employee Inefficiency and Lack of Motivation Representative wastefulness: Lack of inspiration The representatives in Air Arabia were seen as less effective and in this way the organization was assembled to expand its toll to support weight of expanding oil pricesâ [6]â . The primary driver of this issue can be absence of inspiration in the workers towards the company㠢㠢‚⠬㠢„â ¢s development. On the off chance that the workers would have been progressively inspired, they could have been increasingly proficient and in this way the issue of cost climb as a result of high operational expense could have been forestalled. This is an away from of less persuaded work power. (Tuning in, the Doorway to Employee Commitment, 2005) Issue Statement: Most of its representatives need to work under tension fundamentally for the supportability of the association which has raised the degree of worker disappointment in the organization Issue Highlight: Employee Dissatisfaction Representative disappointment: There are various contenders of Air Arabia in minimal effort flight industry which powers representatives to work more enthusiastically with restricted assets. This outcomes in more noteworthy worker disappointment towards the working environment and more representative turnover rate. Innovation: Issue articulation: But all these specialized progressions have a furthest cutoff past which it can't be extended, and by then representative execution comes into picture and must be taken to its most ideal level. Issue Highlight: Employee Training Worker preparing: The issue here is that when new innovation is acquainted in the organization with cut operational costs, the work and desire from the representatives additionally changes a great deal. So there is a reasonable need to worker preparing. Representatives are should have been prepared at new innovation so they can be a piece of company㠢㠢‚⠬㠢„â ¢s cost cutting plan. Worker preparing is a fundamental piece of any association which should be happen periodicallyâ [7]â . Structure: Issue Statement: as worker responsibility is a significant issue and it can't be dealt with by the association without appropriate organizing and it is additionally one of the significant issues looked via Air Arabia Issue Highlight: Leadership Initiative: For the situation, we found that representatives are not dedicated to the association. This is the duty of the pioneer to keep the confidence of the workers in the association. In this way the organization needs its pioneers to take increasingly dynamic job. The pioneers in the organization need to persuade the representatives and to keep up the responsibility of the workers in the organization. The organizing segment in this issue is even more a necessity of a leaderâ [8]â . Issue Statement: Upper administration is confronting an issue to hold its whole structure which is like the instance of Lufthansa Airways. There might be a requirement for an improved arrangement of hierarchical conduct required in such manner that can be furnished with the assistance of appropriate preparing Issue Highlight: Training Preparing: The issue here is that because of the high unsteadiness of work advertise in aircraft industry, the organization can't keep up its ability pool which again is presenting shakiness in its hierarchical structure. This flimsiness should be taken care of by diminishing occupation turnover rate by progressively inspirational preparing to its employeesâ [9]â .

Browns Chemistry The Central Science,15.8 Exercise 1

Earthy colored's Chemistry The Central Science,15.8 Exercise 1 SAT/ACT Prep Online Guides and Tips This posts contains aTeaching Explanation. You can buyChemistry: The Central Sciencehere. Why You Should Trust Me:I’m Dr. Fred Zhang, and I have a bachelor’s certificate in math from Harvard. I’ve piled on hundreds and many long stretches of experienceworking withstudents from 5thgradethroughgraduate school, and I’m enthusiastic about instructing. I’ve read the entire part of the content previously and invested a decent measure of energy contemplating what the best clarification is and what kind of arrangements I would have needed to find in the issue sets I allocated myself when I educated. Exercise: 15.8 Practice Exercise 1 Question: †¦ When 9.2g of solidified $N_2O_4$ is added to a .50L response vessel †¦ [What is the estimation of $K_c$] Section 1: Approaching the Problem The inquiry is posing for a harmony consistent ($K_c$). We need to know$K_c$. By and large, we can know the balance steady ONLY IF we can make sense of the harmony centralizations of the species (nitrous oxide and dinitrogen tetraoxide): $$K_c = [NO_2]^2/[N_2O_4]$$ Along these lines, the whole game to making sense of the harmony steady here is to make sense of the balance focuses. We are as of now given that in harmony, the grouping of $[N_2O_4]$=.057 molar. So we have a large portion of the riddle: $$K_c = [NO_2]^2/.057$$ The other portion of the riddle if making sense of the harmony fixation $[NO_2]$. Unfortunately, the inquiry doesn’tjust give us this. Be that as it may, we have a snippet of data about as great, which is the beginning (starting) sum of$[N_2O_4]$. Since we know the response condition, thekey now is to go from introductory sum of$[N_2O_4]$ to the last (harmony) focus $[NO_2]$. Section 2: Converting Grams to Molar We are given that the response began with 9.2g of $N_2O_4$ in a 0.50L response vessel. For harmony estimations, we for the most part need to know groupings of types atoms, rather than genuine mass or volume. We apply stoichiometry here and convert grams per liter to molarity utilizing molar mass. We go through the occasional table to look the molar mass of$N_2O_4$ is 92.01 grams per mole. We get that: $$(9.2g N_2O_4)/(0.50L) *(1 mol)/(92.01 g N_2O_4) = (0.100mol)/L = 0.200 molar$$ Accordingly the underlying focus of$N_2O_4$is 0.200 molar, and composed as [$N_2O_4$]=.200 Section 3: Running the Reaction Since we know the beginning focus, we need to get to definite fixations. The mathematical condition that connects the two is the condition of response: $$N_2O_4 (g) ↠2 NO_2 (g)$$ This implies for each atom of$N_2O_4$ we get two particles of $NO_2$. As the response goes ahead, when$N_2O_4$ diminishes by $x$ molar,$NO_2$ increments by $2x$ molar. The focus table is at that point: $N_2O_4 (g)$ $2 NO_2 (g)$ Starting Concentration (M) 0.200 0 Change in Concentration (M) - x +2x Balance Concentration (M) 0.200-x 2x Section 4: Calculating the Equilibrium We are given that the balance fixation of[$N_2O_4$]=.057 molar. The fixation table above gives the balance focus of[$N_2O_4$]=0.200-x, so we simply liken the two and explain for x. 0.200-x = 0.057 x = .143 Since we know x, 2x = .268 Or on the other hand that in balance, $[NO_2]=.268$ To compute the balance steady Kc, we plug in the data above: $$K_c = [NO_2]^2/[N_2O_4]=.268^2/.057= 1.43$$ In this manner, the correct answer is d) 1.4 Video Solution Get full reading material answers for just $5/month. PrepScholar Solutions has bit by bit arrangements that show you basic ideas and assist you with acing your tests. With 1000+ top writings for math, science, material science, designing, financial aspects, and that's only the tip of the iceberg, we spread every single mainstream course in the nation, including Stewart's Calculus. Attempt a 7-day free preliminary to look at it.

Racial Disparity in Criminal Justice System Essay

Presentation Twenty-five percent of the world’s jail populace, 2.5 million individuals, are held in American corrective organizations. (ACLU, 2008). 60% of those imprisoned are racial and ethnic minorities. These figures imply that 2.3% of every single African American are imprisoned. The level of whites admitted to jail is 0.4% of whites and Hispanics, 0.7%. (Related Press, 2007; Bonczar, 2003; Mauer and King, 2007; ACLU, 2008; Bridges and Sheen, 1998;). One of the essential supporters of this gross lopsidedness of imprisonment of blacks is the aftereffect of â€Å"the war on drugs† and â€Å"tough on crime† activities that were set up in the 80’s. The forceful law requirement procedures of The Anti-Drug Abuse Act of 1986, excessively captured, indicted, and imprisoned a huge number of blacks for moderately minor peaceful medication offenses when contrasted with white guilty parties. The emotional heightening of imprisonment for tranquilize offenses was joined by significant racial incongruities. Blacks were imprisoned at a horribly unbalanced rate to white Americans and blacks got a lot harsher and longer sentences, 14.5% longer, making racial difference inside the criminal equity framework (Alexander, 2010; Austin, et al.; Georges-Abeyie, 2006; Gonzã ¡lez and Chang, 2011; Lynch and William, 1997; Mauer, 2007; Mauer and King, 2007; Spohn, 2000 (Alexander, 2010, Associated Press, 2007, Mauer M. 2009; Mauer M., 2008; Spohn, 2000) Mass detainment works more like a station framework than an arrangement of wrongdoing anticipation fills a similar need as pre-Civil War servitude and the post-Civil War Jim Crow laws: to keep up a racial standing framework: a framework intended to keep a racial gathering secured in a sub-par position by law and customs. (Alexander, 2010) While researchers have since quite a while ago broke down the association among race and America’s criminal equity framework, contend that our developing correctional framework, with its dark tinge, comprises nothing not exactly another type of Jim Crow. There are scholars that vibe the analogy’s nearsighted spotlight on the War on Drugs redirects us from examining vicious crimeâ€an oversight when talking about mass collaboration in the United States. (James Forman) There is no debate regarding the degree of the acceleration in criminalization and detainment in the United States in the 40-year war on drugs. That vicious guilty parties make up a majority ofâ the jail populace, yet look into has indicated that the inconsistent implementation of required strategies set up, dark guys got longer terms than whites for comparative medication offenses, 14.5% longer, this makes the degree of mass imprisonment that racial uniqueness inside the criminal equity framework. ). Ta ke a gander at states in there Midwest and upper east have the best dark to-white difference in detainment. So when states as Iowa, the tenth most secure state in the US, 91.3% of the populace is White (88.7% non-Hispanic),and 2.9% is Black or African American, how is it for each 100,000 individuals Iowa detains 309 white and 4200 are dark, detaining dark at multiple times the pace of whites. The inconsistent implementation of compulsory strategies set up, dark guys got longer terms than whites for comparable medication offenses, 14.5% longer, this makes the degree of mass detainment that racial difference inside the criminal equity framework. Supporting information shows the phenomenal increments in a few conditions of nonwhite tranquilize wrongdoers focused on jail getting harsher sentences for comparable medication offenses. (Alexander, 2010; Tonry, 1994 (ACLU, 2008; Alexander, 2010; Green, 2012Lacey, 2010; Bonczar, 2003; Glaze and Herberman, 2010; Mauer, 2009; Mauer, 2008; M Mauer and King (2007);Russell-Brown, 2008; Mauer and King 2007; The Institute for Economics and Peace, 2012; Pet ersilia,1983; Loury, 2010; Russell-Brown, 2008). There have been concentrates in hypothetical establishment and methodological advancement to survey the disproportionality in imprisonment of racial minorities. Research has dispersed the affirmation that blacks are disproportionality condemned and imprisoned due exclusively to differential wrongdoing commission rates. All entertainers inside the criminal equity framework are under the dream, or affectation, of objectivity in the criminal equity framework. (Spohn, 2000; Russell-Brown, 2008) in light of this hole in writing, the present investigation will concentrate only on the reliable examples demonstrating that wrongdoer race works legitimately through different components, capturing official, earlier record, kind of wrongdoing, pretrial status or sort of attitude, or communicates with different factors that are themselves identified with racial difference. I will likewise endeavor to decide why these disproportionalities exist by looking at the criminal equity framework strategie s and practices that have contributed in ongoing decades to the lopsided overrepresentation of minorities in the criminal equity framework. Writing Review Criminologist and social-political geographer Daniel E. Georges-Abeyie presented the idea and hypothesis of petit politically-sanctioned racial segregation in criminal equity and adolescent equity in 1990 to portray oppressive, optional acts by law authorization, prison guards, and legal scholars that favorable position or drawback an individual, or people, on grounds of their personality qualities, for example, race, ethnicity, sex, sex, sexual direction, age, religion, or nationality Georges-Abeyie Petit Apartheid Social Distance Severity Scale to anticipate criminal equity process results when the character attributes of those creation optional choices and those affected are comparative or unique. Petit Apartheid Social Distance Severity Scale. His plain meeting with Justice Bruce Wright affirmed that every on-screen character brings his own inclination into his obligations in the criminal equity framework. New York State Supreme Court Justice the Honorable McM. Bruce Wright, creator of Black Robes, White Justice (1992), a criminal equity advocate, accepted that an appointed authority ought to deliberately be â€Å"Black, Hispanic, female, common laborers, et cetera†, while mediating. Judge Wright accepted that all appointed authorities showed their social, social, racial, ethnic, sexual orientation, and social class predispositions while settling. We are completely affected by life encounters. He gave a model, a particular appointed authority, who might normally, proudly and grandiosity, announced that he â€Å"quickly evaluated a defendant† as the litigant was driven into the court in chains, by taking note of the aura, walk, non-verbal communication, and general physical appearance of the respondent before the defendant’s lawyer, or the litigant, articulated a solitary word. What dismayed Judge Wright was not the examining of that respondent but rather the forswearing of the phenomenologically sifted judgment, which went with that perception. (Georges-Abeyie, 2006) Multi factors financial, individual inclination and what are viewed as unobtrusive predisposition, guilty party age and sexual orientation, are central point in the degree of racial divergence inside the criminal equity framework. (Georges-Abeyie, 2006;; Austin, et al., 2012;Bonczar, 2003; Brewer and Heitzeg; Glaze and Herberman, 2012; Green, 2012; Lacey,2010; Gonzã ¡lez and Chang, 2011; Lee and Vukich, 2001;Loury, 2010)Mauer and King, 2007; Petersilia, 1983; Spohn, 2000; Tonry, 1994; Marc Mauer has been giving an account of racial dissimilarity since 1975 report on racial divergence and mass detainment in the criminal equity framework. His 1995 report drove the New York Times to editorialize that the report â€Å"should set off alerts from the White House to city corridors †and help turn around the thought that we can detain out of crucial social problems.† Finding proof of direct oppression minorities in the job of race, expectation, and attentiveness in the criminal equity framework (Baradaran, 2013; Mauer M. 2009) Research has demonstrated that the principal purpose of segregation that harasses the framework is contact with the police. Police capture dark litigants more regularly for wrongdoings than white respondents. (Mauer and King, 2007) Spohn in his report, Thirty Years of Prison Reform: the race for a killing sentence process,† found that â€Å"a particular type† of minority guilty parties, maybe in light of the fact that they ar e seen as being progressively hazardous, are singled out for capture and harsher treatment. These markers are Blacks and Hispanics who are youthful, male, and jobless are especially more probable than their white partners to be condemned to jail and in certain purviews, they additionally get longer sentences or differential advantages from rule takeoffs. There is additionally proof that minorities indicted for tranquilize offenses, those with longer earlier criminal records, the individuals who defraud whites, and the individuals who will not concede or can't make sure about pretrial discharge are rebuffed more seriously than correspondingly arranged whites. (Spohn, 2000) Crime rates, law authorization needs, condemning enactment and different components assume a job in making racial variations in detainment. (Roth, 2001). The examiners, more than anyâ other authorities in the criminal equity framework, have the most immediate effect on racial incongruities, and therefore, must bear the most duty in curing them. (Davis, 1998) Race (and specifically racial generalizations) assumes a job in the decisions and dynamic by the entirety of the members inside the criminal equity framework. The impact of an individual’s predisposition is unobtrusive and regularly imperceptible in some random case, however its belongings are critical and recognizable after some time. At the point when policymakers decide strategy, when official entertainers practice attentiveness, and when residents proffer declaration or jury-administration, inclination regularly assumes a job. (Georges-Abeyie, 2006). In January of 2000, 19-year-old Jason Williams was indicted for selling a sum of 1/8 oz. of cocaine on four separate events. In spite of the fact that he had no earlier feelings, the Texas youth was condemned to 45 years in jail und

Rewriting an introduction for a chemistry paper Essay

Revising a presentation for a science paper - Essay Example This paper, in this manner, presents far reaching rules for improving students’ information on the fundamental writing in science and their capacities to compose for science crowd. This examination centers around distinguishing a subset of abilities that best in class science understudies require to compose their first expert diaries. These aptitudes incorporate composing shows, crowd and reason, and sentence structure and mechanics. An example of in excess of 300 science understudies from 16 schools and colleges, somewhere in the range of 2004 and 2006, took a composing test to choose abilities that compare to the three segments. The outcomes showed that the members scored 80 percent to abilities identified with sentence structure and mechanics, 45 percent to composing shows, and 40 percent to crowd and reason. So as to improve students’ needs, we proposed a composing exercise that basically focused on composing show and crowd and reason. This action is clarified, in the body sections, and the recommended rules are additionally demonstrated. This paper is finished up by giving suggestions to actualizing these exercises, in science

Administration Decisions Essay Example | Topics and Well Written Essays - 1750 words

Organization Decisions - Essay Example A school can capacity without limit if the families and the network it is built up are included. One sort of school, a network school is interesting in that it remembers for its program an incorporated model that considers partners in the network, for example, accomplices, managers, instructors, guardians and understudies (Jacobson, Hodges, and Martin 18). A people group school doesn't just maintain the scholastics and youth improvement, yet in addition support for the family, award of social administrations and advancement of the network all in all (18). In working with accomplices, a school network perceives the various needs of understudies both in scholastic and non-scholarly circles (20). In this manner, the school site group progresses in the direction of the arrangement of exercises with the vision of the school. The accomplices thusly work in compatibility with the all out progress plan of the school (20). The job of the head in the school and the network can't be overemphasi zed. The chief must know that the network school has a place with the network and ought to associate with the last for all out progress (20). Regarding this, the chief should invite the assets offered by the partners and accomplices of the school (20). ... The School of Cooperative Technical Education (under the NYC Department of Education), then again, gives profession preparing to aptitudes advancement to grades 11 and 12 understudies. The CAS Bronx Family Center additionally gives comprehensive physical, dental and psychological wellness finding to the two understudies and guardians of Fannie Lou. The wellbeing teachers of CAS prompt understudies on wellbeing and forestalling pregnancy. The social specialists situated in the school give psychological well-being exhorts and mediation administrations during emergency. The school gives crisis help to the group of an understudy who is ousted from home. The Oyler Elementary School (in Cincinnati, Ohio) was changed over into a network school that incorporates secondary school offering. This was made conceivable through the banding together of families and individuals from the network with the Cincinnati Public Schools (20). The change of the school into a network school that permitted it to offer a K-12 program empowered understudies to join up with secondary school just because. Already, no understudy in the area had the option to benefit of secondary school training. The Cincinnati Health Department has a center inside the school with the goal that understudies can benefit of wellbeing, dental and vision care administrations (21). Coaching and instructional exercise administrations are given by in excess of 400 volunteers who visit the school week by week to understudies on an individual premise. The school likewise banded together with the Cincinnati Early Learning Centers and different accomplices to offer help to babies, kids and their folks. In Glencliff High School, changing it into a network school set up has permitted it support various projects together with its accomplices, for example, the

Importance Of Computer Automation To Insurance Companies Finance Essay - Free Essay Example

The importance of programming is of prime value for Actuarial Science and for the actuarial profession. The complex calculations merged with routine task based calculations have made programming a viable source for automation. In this dissertation, we show how the programming language, R can be used for claim models to compute aggregate claims using poisson, binomial and negative binomial distributions. We also demonstrate how to use MortalitySmooth package to compute deaths and exposure data suitable for smoothing mortality data. An essential aspect of this method is that smoothening of data allows forecasting of mortality data to use in computing annuities for different countries. We explain these methods using Danish dataset for aggregate claims and Human mortality database (HMD , https://www.mortality.org), a collection of mortality data of various developed countries. Chapter 1 Introduction The insurance firms functions making insurance products attains profitability through charging premiums surpassing overall expenses of the firm and making wise investment decisions in maximizing returns under optimal risk conditions. The method of charging premiums depends on so many underlying factors such as number of policy holders, number of claims, amount of claims, health condition, age, gender of the policy holder and so on. Some of these factors such as loss aggregate claims and human mortality rates have adverse impact on determining the premium calculation to remain solvent. Likewise, these factor need to be modelled using large amount of data, loads of simulations and complex algorithms to determine and manage risk. In this dissertation we shall consider two important factors affecting the premiums, the aggregate loss claims and human mortality. We shall use theoretical simulations using R and use Danish data to model aggregate claims and human mortality database to obtain human mortality rates and smoothen to price life insurance products respectively. In chapter 2 we shall examine the concepts of compounds distribution in modelling aggregate claim and perform simulations of the compound distribution using R packages such as MASS and Actuar. Finally we shall analyse Danish loss insurance data from 1980 to 1990 and fit appropriate distributions using customized generically implemented R methods. In chapter 3 we shall explain briefly on concepts of graduation, generalised linear models and smoothening techniques using B-splines. We shall obtain deaths and exposure data from human mortality database for selected countries Sweden and Scotland and shall implement mortality rates smoothing using mortalitysmooth package. We compare the mortality rates based on various sets such as Males and females for specific country or total mortality rates across countries like Sweden and Scotland for a given time frame ranging age wise or year wise. In chapter 4 we shall look into various life insurance and pension related products widely used in the insurance industry and construct life tables and commutation functions to implement annuity values. Finally chapter 5 we present concluding comments to the dissertation. Chapter 2 Aggregate Claim distribution 2.1 Background Insurance based companies implement numerous techniques to evaluate the underlying risk of their assets, products and liabilities on a day- to-day basis for many purposes. These include Computation of premiums Initial reserving to cover the cost of future liabilities Maintain solvency Reinsurance agreement to protect from large claims In general, the occurrence of claims is highly uncertain and has underlying impact on each of the above. Thus modelling total claims is of high importance to ascertain risk. In this chapter we shall define claim distributions and aggregate claims distributions and discuss some probabilistic distributions fitting the model. 2.2 Modelling Aggregate Claims The dynamics of insurance industry has different effects on the number of claims and amount of claims. For instance, Expanding insurance business would have proportional increase on number of claims but negligible or no impact on amount of claims. Conversely, cost control initiatives, technology innovations have adverse effect on amount of claims but has zero effect on number of claims. Consequently, the aggregate claim is modelled based on the assumption that the number of claims occurring and amount of claims are modelled independently. 2.2.1 Compound distribution model We define compound distribution as S Random variable denoting the total claims occurring in a fixed period of time. Denote the claim amount representing the i-th claim. N Non-negative, independent random variable denoting number of claims occurring in a time period. Further, is a sequence of i.i.d random variables with probability density function given by and cumulative density function by with probability of 0 is 1 for 1iN. Then we obtain the aggregate claims S as follows With Expectation and variance of S found as follows Thus S, the aggregate claims is computed using Collective Risk Model and follows compound distribution. (pg 86 Non-life actuarial model theory, methods and evaluation) 2.3 Compound distribution for aggregate claims As discussed in Section 2.1 S, follows compound distribution. were N, the number of claims is the primary distribution and X, the amount of claims being secondary distribution In this section we shall describe the three main compound distributions widely used to model aggregate claims models. The primary distribution, N can be modelled based on non-negative integer valued distributions like poisson, binomial and negative binomial. The selection of a distribution depends from case to case. 2.3.1 Compound Poisson distribution The Poisson distribution is referred to distribution of occurrence of rare events, Number of accidents per person, number of claims per insurance policy and number of defects found in product manufacturing are some of the real time examples of Poisson distribution. Here, the primary distribution N has a Poisson distribution denoted by N ~ P(ÃÆ'Ã… ½Ãƒâ€šÃ‚ » with parameter ÃÆ'Ã… ½Ãƒâ€šÃ‚ ». The probability density function, expectation and variance are given as follows for x=0,1. Then S has a compound Poisson distribution with parameters ÃÆ'Ã… ½Ãƒâ€šÃ‚ » and denoted as follows S ~ CP(ÃÆ'Ã… ½Ãƒâ€šÃ‚ », and 2.3.2 Compound Binomial distribution The binomial distribution is referred to distribution of number of success occurring in an event, the number of males in a company, number of defective components in random sample from a production process is real time examples representing this distribution. The compound binomial distribution is a natural choice to model aggregate claims when there is an upper limit on the number of claims in a given time period. Here, the primary distribution N has a binomial distribution with parameters n and p denoted by N ~ B(n,p. The probability density function, expectation and variance are given as follows For x=0,1,2.n Then S has a compound binomial distribution with parameters ÃÆ'Ã… ½Ãƒâ€šÃ‚ » and denoted as follows S ~ CB(n, p , -p) 2.3.3 Compound Negative Binomial distribution The compound negative binomial distribution models aggregate claim models. The variance of negative binomial is greater than its mean and thus we can use negative binomial over Poisson distribution if the data has greater variance than its mean. This distribution provides a better fit to the data. Here, the primary distribution N has a negative binomial distribution with parameters n and p denoted by N ~ NB(n,p with n0 and 0p1. The probability density function, expectation and variance are given as follows for x=0,1,2. / Then S has a compound negative binomial distribution with parameters ÃÆ'Ã… ½Ãƒâ€šÃ‚ » and denoted as follows S ~ CNB(n,p, 2.4 Secondary distributions claim amount distributions. In Section 2.3, we defined the three different compound distributions widely used. In this section, we shall define the generally used distributions to model secondary distributions for claim amounts. We use positive skewed distributions. Some of these distributions include Weibull distribution used frequently in engineering applications. we shall also look into specific distributions such as Pareto and lognormal which are widely used to study loss distributions. 2.4.1 Pareto Distribution The distribution is named after Vilfredo Pareto who used it in modelling economic welfares. It is used these days to model income distribution in economics. The random variable X has a Pareto distribution with parameters and ÃÆ'Ã… ½Ãƒâ€šÃ‚ » where, ÃÆ'Ã… ½Ãƒâ€šÃ‚ » 0 and is denoted by X~ ( or X ~ Pareto(, ÃÆ'Ã… ½Ãƒâ€šÃ‚ ») The probability density function, expectation and variance are given as follows For x0 2.4.2 Log normal Distribution The random variable X has a Log normal distribution with parameters and where, 0 and is denoted by X ~ LN(, ), Where, and are the mean and variance of Log(X). The log normal distribution has a positive skew and is a very good distribution to model claim amount. The probability density function, expectation and variance are given as follows For x0 and 2.4.3 Gamma distribution The gamma distribution is very useful to model claim amount distribution it has , the shape parameter and ÃÆ'Ã… ½Ãƒâ€šÃ‚ » the scale parameter. The random variable X has a Gamma distribution with parameters and ÃÆ'Ã… ½Ãƒâ€šÃ‚ » where, ÃÆ'Ã… ½Ãƒâ€šÃ‚ » 0 and is denoted by X~ ( or X ~ Gamma(, ÃÆ'Ã… ½Ãƒâ€šÃ‚ ») The probability density function, expectation and variance are given as follows For x0 2.4.4 Weibull Distribution The Weibull distribution is extreme valued distributions, because of its survival function it is used widely in modelling lifetimes. The random variable X has a Weibull distribution with parameters and ÃÆ'Ã… ½Ãƒâ€šÃ‚ » where, ÃÆ'Ã… ½Ãƒâ€šÃ‚ » 0 and is denoted by X~ ( The probability density function, expectation and variance are given as follows For x0 2.5 Simulation of Aggregate claims using R In section 2.3 we discussed about aggregate claims and the various compound distributions used to model it. In this section we shall perform random simulation using R program. 2.5.1 Simulation using R The simulation of aggregate claims was implemented using packages like Actuar, MASS. The generic R code available in Programs/Aggregate_Claims_Methods.r implements simulation of random generated aggregate claim of any compound distribution samples. The following R code below generates simulated aggregate claim data for Compound Poisson distribution with gamma as the claim distribution denoted by CP(10,. require(actuar) require(MASS) source(Programs/Aggregate_Claims_Methods.r) Sim.Sample = SimulateAggregateClaims (ClaimNo.Dist=pois, ClaimNo.Param =list(lambda=10),ClaimAmount.Dist=gamma,ClaimAmount.Param= list(shape = 1, rate = 1),No.Samples=2000 ) names(Sim.Sample) The SimulateAggregateClaims method in Programs/Aggregate_Claims_Methods.r generates and returns simulated aggregate samples along with expected and observed moments. The simulated data can then be used to perform various tests, comparisons and plots. 2.5.2 Comparison of Moments The moments of expected and observed are compared to test the correctness of the data. The following R code returns the expected and observed mean and variance of the simulated data Respectively. Sim.Sample$Exp.Mean;Sim.Sample$Exp.Variance Sim.Sample$Obs.Mean;Sim.Sample$Obs.Variance Table 2.1 Comparison of Observed and Expected moments for different sample size. The Table 2.1 above shows the simulated values for different Sample size. Clearly the observed and expected moments are similar and the difference between them converges as Number of sample increases. 2.5.3 Histogram with curve fitting distributions Histograms can provide useful information on skewness, information on extreme points in the data, the outliers and can be graphically measured or compared with shapes of standard distributions. The figure 2.1 below shows the fitted histogram of simulated data compared with standard distributions like Weibull, Normal, Lognormal and Gamma respectively. Figure 2.1 Histogram of simulated aggregate claims with fitted standard distribution curves. Figure 2.1 represents the histogram of the stimulated data along with the fitted curves for different distributions. The histogram is plotted by dividing them in to breaks of 50. The simulated data is then fitted using the fitdistr() function in the MASS package and fitted for various distributions like Normal,Lognormal,Gamma and Weibull distribution. The following R program describes how the fitdistr method is used to compute the Gamma parameters and plot the respective curve as described in Figure 2.1 gamma = fitdistr(Agg.Claims,gamma) Shape = gamma$estimate[1] Rate= gamma$estimate[2] Scale=1/Rate Left = min(Agg.Claims) Right = max(Agg.Claims) Seq = seq(Left,Right,by= 0.01) lines(Seq,dgamma(Seq,shape=Shape, rate= Rate, scale=Scale), col = blue) 2.5.4 Goodness of fit The goodness of fit compare the closeness of expected and observed values to conclude whether it is reasonable to accept that the random sample fits a standard distribution or not. It is type of hypothesis testing were the hypotheses are defined as follows. : Data fits with the standard distribution : Data does not fit with the standard distribution The chi-square test is one of the ways to test goodness of fit. The test uses histogram and compares it with the fitted density. It is used by grouping data into different intervals using k breaks. The breaks are computed using quantiles. This computes the expected frequency,. , the observed frequency is calculated using the product of difference of the c.d.f with sample size. The test statistic is defined as Where is the observed frequency and is expected frequency for k breaks respectively. To perform simulation we shall use breaks of 100 to split the data into equal cells of 100 and use histogram count to group the data based on the observed values. Large values of leads to rejecting null hypothesis The test statistic follows distribution with k-p-1 degrees of freedom where p is the number of parameters in sample data. The p-value is computed using 1- pchisq() and is accepted if p-value is greater than the significance level . The following R code computes chi-square test Test.ChiSq=PerformChiSquareTest( Samples.Claims= Sim.Sample$AggregateClaims,No.Samples=N.Samples) Test.ChiSq$DistName Test.ChiSq$X2Val;Test.ChiSq$pvalue Test.ChiSq$Est1; Test.ChiSq$Est2 Table 2.3 Chi-Square and p-value for compound Poisson distribution The highest p-value signifies better fit of data with the standard distribution. Weibull distribution is a better fit with the following parameters shape =2.348 and scale = 11.32. 2.6 Fitting Danish Data 2.6.1 The Danish data source of information In this section we shall use a statistical model and fit a compound distribution to compute aggregate claims using historical data. Fitting data into a probability distribution using R is an interesting exercise, and is worth quoting All models are wrong, some models are useful. In previous section we explained fitting distribution, comparison of moments and goodness of fit to simulated data. The data source used is Danish data composed from Copenhagen Reinsurance and contains over 2000 fire loss claims details recorded during 1980 to 1990 period of time. This data is adjusted for inflation replicating 1985 values and are expressed in Danish Krone (DKK) currencies in millions. The data recorded are large values and are adjusted for inflation. There are 2167 rows of data over 11 years. Grouping the data over years results in 11 aggregate samples of data. This would be insufficient information to fit and plot the distribution. Therefore, the data is grouped month-wise aggregating to 132 samples. The expectation and variance of the aggregate claims are 55.572 and 1440.7 respectively. The figure 2.2 shows the time series plot against the claim numbers inferring the different claims occurred monthly from 1980 to 1990, it also shows the extreme values of loss claims and the time of occurrence. There are no seasonal effects on the data as the 2 sample test for summer and winter data is compared and the t-test value infers there is no difference and conclude that there is no seasonal variation. Figure 2.2 Time series plot of Danish fire loss insurance data month wise starting 1980-1990. The data is plotted and fitted into an histogram using fitdistr() function in MASS package of R. 2.6.2 Analysis of Danish data We shall do the following steps to analyse and fit the data. Obtain the claim numbers and loss aggregate claim data month wise. Choose primary distribution to be Poisson or negative binomial and use fitdistr() function to obtain the parameters. Assume Gamma distribution as the default loss claim distribution and use fitdistr() to obtain the shape and rate parameters. Simulate for 1000 samples using section 2.5.1, also plot the histogram along with the fitted standard distributions as described in section 2.5.2. Perform chi-square test to identify the optimal fit and obtain the distribution parameters. Finally implement another simulation using the primary distribution and fitted secondary distribution. 2.6.3 R Implementation We will do the following to implement R. The Danish data is assumed to take gamma distribution Plot the computed aggregate claims and use fitdistr() to get the parameters using gamma or lognormal. Now, using generic R implementation discussed in Section 2.5 we simulate using the new dataset and finally fit with standard distributions. The following R code reads the Danish data available in DataDanishData.txt, segregate the claims month and year wise, to calculate sample mean and variance and plots the histogram with fitted standard distributions. require(MASS) source(Programs/Aggregate_Claims_Methods.r) Danish.Data = ComputeAggClaimsFromData(Data/DanishData.txt) Danish.Data$Agg.ClaimData = round(Danish.Data$Agg.ClaimData, digits = 0) #mean(Danish.Data$Agg.ClaimData) #var(Danish.Data$Agg.ClaimData) #Danish.Data$Agg.ClaimData #mean(Danish.Data$Agg.ClaimNos) #var(Danish.Data$Agg.ClaimNos) Figure 2.3 Actual Danish fire loss data fitted with standard distributions of 132 samples. In the initial case N, the primary distribution is assumed to be Negative Binomial distributed with parameter; k= 25.32 and p=.6067 and the secondary distribution is assumed to be gamma distribution with parameters; Shape =3.6559 and rate =.065817. We simulate using 1000 samples and obtain aggregate claim samples using Section 2.5.1. The plot and chi square test values are defined below as follows. The generic function PerformChiSquareTest, previously discussed in Section 2.4 is used here to compute values of and p-value pertaining to = distribution. The corresponding values are tabulated in table 2.2 below. Figure 2.4 Histogram of simulated samples of Danish data fitted with standard distributions The figure 2.4 shows simulated samples of Danish data calculated for sample size 1000, The figure also shows the different distribution curves fitted to the simulated data. These results suggest that the best possible choice of model is Gamma distribution with parameters Shape = 8.446 and Rate = .00931 Chapter 3 Survival models Graduation In the previous chapter 2, we discussed about aggregate claims and how it can be modelled and simulated using R programming. In this chapter we shall discuss on one of the important factors which has direct impact on arise of a claim, the human mortality. Life insurance companies use this factor to model risk arising out of claims. We shall analyse and investigate the crude data presented in human mortality database for specific countries like Scotland and Sweden and use statistical techniques. Mortality smooth package is used in smoothing the data based on Bayesian information criterion BIC, a technique used to determine smoothing parameter; we shall also plot the data. Finally we shall conclude by performing comparison of mortality of two countries based on time. 3.1 Introduction Mortality data in simple terms is recording of deaths of species defined in a specific set. This collection of data could vary based on different variables or sets such as sex, age, years, geographical location and beings. In this section we shall use human data grouped based on population of countries, sex, ages and years. Human mortality in urban nations has improved significantly over the past few centuries. This has attributed largely due to improved standard of living and national health services to the public, but in latter decades there has been tremendous improvement in health care in recent measures which has made strong demographic and actuarial implications. Here we use human mortality data and analyse mortality trend compute life tables and price different annuity products. 3.2 Sources of Data Human mortality database (HMD) is used to extract data related to deaths and exposure. These data are collected from national statistical offices. In this dissertation we shall look into two countries Sweden and Scotland data for specific ages and years. The data for specific countries Sweden and Scotland are downloaded. The deaths and exposure data is downloaded from HMD under Sweden Deaths https://www.mortality.org/hmd/SWE/STATS/Deaths_1x1.txt They are downloaded and saved as .txt data files in the respective hard disk under /Data/Conutryname_deaths.txt and /Data/Conutryname_exposures.txt respectively. In general the data availability and formats vary over countries and time. The female and male death and exposure data are shared from raw data. The total column in the data source is calculated using weighted average based on the relative size of the two groups male and female at a given time. 3.3 Gompertz law graduation A well-known actuary, Benjamin Gompertz observed that over a long period of human life time, the force of mortality increases geometrically with age. This was modelled for single year of life. The Gompertz model is linear on the log scale. The Gompertz law states that the mortality rate increases in a geometric progression. Hence when death rates are A0 B1 And the liner model is fitted by taking log both sides. = a + bx Where a = and b = The corresponding quadratic model is given as follows 3.3.1 Generalized Linear models are P-Splines in smoothing data Generalized Linear Models (GLM) are an extension of the linear models that allows models to be fit to data that follow probability distributions like Poisson, Binomial, and etc. If is the number of deaths at age x and is central exposed to risk then By maximum likelihood estimate we have and by GLM, follows Poisson distribution denoted by with a + bx We shall use P-splines techniques in smoothing the data. As mentioned above the GLM with number of deaths follows Poisson distribution, we fit a quadratic regression using exposure as the offset parameter. The splines are piecewise polynomials usually cubic and they are joined using the property of second derivatives being equal at those points, these joints are defined as knots to fit data. It uses B-splines regression matrix. A penalty function of order linear or quadratic or cubic is used to penalize the irregular behaviour of data by placing a penalty difference. This function is then used in the log likelihood along with smoothing parameter .The equations are maximised to obtain smoothing data. Larger the value of implies smoother is the function but more deviance. Thus, optimal value of is chosen to balance deviance and model complexity. is evaluated using various techniques such as BIC Bayesian information criterion and AIC Akaikes information criterion techniques. Mortalitysmooth package in R implements the techniques mentioned above in smoothing data, There are different options or choices to smoothen using p-splines, The number of knots ndx ,the degree of p-spine whether linear,quadratic or cubic bdeg and the smoothning parameter lamda. The mortality smooth methods fits a P-spline model with equally-spaced B-splines along x There are four possible methods in this package to smooth data, the default value being set is BIC. AIC minimization is also available but BIC provides better outcome for large values. In this dissertation, we shall smoothen the data using default option BIC and using lamda value. 3.4 MortalitySmooth Package in R program implementation In this section we describe the generic implementation of using R programming to read deaths and exposure data from human mortality database and use MortalitySmooth package to smoothen the data based on p-splines. The following code presented below loads the require(MortalitySmooth) source(Programs/Graduation_Methods.r) Age -30:80; Year - 1959:1999 country -scotland ;Sex - Males death =LoadHMDData(country,Age,Year,Deaths,Sex ) exposure =LoadHMDData(country,Age,Year,Exposures,Sex ) FilParam.Val -40 Hmd.SmoothData =SmoothenHMDDataset(Age,Year,death,exposure) XAxis - Year YAxis-log(fitted(Hmd.SmoothData$Smoothfit.BIC)[Age==FilParam.Val,]/exposure[Age==FilParam.Val,]) plotHMDDataset(XAxis ,log(death[Age==FilParam.Val,]/exposure[Age==FilParam.Val,]) ,MainDesc,Xlab,Ylab,legend.loc ) DrawlineHMDDataset(XAxis , YAxis ) The MortalitySmooth package is loaded and the generic implementation of methods to execute graduation smoothening is available in Programs/Graduation_Methods.r. The step by step description of the code is explained below. Step:1 Load Human Mortality data Method Name LoadHMDData Description Return an object of Matrix type which is a mxn dimension with m representing number of Ages and n representing number of years. This object is specifically formatted to be used in Mortality2Dsmooth function. Implementation LoadHMDData(Country,Age,Year,Type,Sex) Arguments Country Name of the country for which data to be loaded. If country is Denmark,Sweden,Switzerland or Japan the SelectHMDData function of MortalitySmooth package is called internally. Age Vector for the number of rows defined in the matrix object. There must be atleast one value. Year Vector for the number of columns defined in the matrix object. There must be atleast one value. Type A value which specifies the type of data to be loaded from Human mortality database. It can take values as Deaths or Exposures Sex An optional filter value based on which data is loaded into the matrix object. It can take values Males, Females and Total. Default value being Total Details The method LoadHMDData in Programs/Graduation_Methods.r reads the data availale in the directory Data to load deaths or exposure for the given parameters. The data can be filtered based on Country, Age, Year, Type based on Deaths or Exposures and lastly by Sex. Figure: 3.1 Format of matrix objects Death and Exposure. The Figure 3.1 shows the format used in objects Death and Exposure to store data. A matrix object representing Age in rows and Years in column. The MortalitySmooth package contains certain features for specific countries listed in the package. They are Denmark,Switzerland,Sweden and Japan. These data for these countries can be directly accessed by a predefined function SelectHMDData. LoadHMDData function checks the value of the variable country and if Country is equal to any of the 4 countries mentioned in the mortalitysmooth package then SelectHMDData method is internally called or else customized generic function is called to return the objects. The return objects format in both functions remains exactly the same. Step 2: Smoothen HMD Dataset Method Name SmoothenHMDDataset Description Return a list of smoothened object based BIC and Lamda of matrix object type which is a mxn dimension with m representing number of Ages and n representing number of years. This object is specifically formatted to be used in Mortality2Dsmooth function. Returns a list of objects of type Mort2Dsmooth which is a two-dimensional P-splines smooth of the input data and order fixed to be default. These objects are customized for mortality data only. Smoothfit.BIC and Smoothfit.fitLAM objects are returned along with fitBIC.Data fitted values. SmoothenHMDDataset (Xaxis,YAxis,ZAxis,Offset.Param) Arguments Xaxis Vector for the abscissa of data used in the function Mortality2Dsmooth in MortalitySmooth package in R. Here Age vector is value of XAxis. Yaxis Vector for the ordinate of data used in the function Mortality2Dsmooth in MortalitySmooth package in R. Here Year vector is value of YAxis. .ZAxis Matrix Count response used in the function Mortality2Dsmooth in MortalitySmooth package in R. Here Death is the matrix object value for ZAxis and dimensions of ZAxis must correspond to the length of XAxis and YAxis. Offset.Param A Matrix with prior known values to be included in the linear predictor during fitting the 2d data. Here exposure is the matrix object value and is the linear predictor. Details. The method SmoothenHMDDataset in Programs/Graduation_Methods.r smoothens the data based on the death and exposure objects loaded as defined above in step 1. The Age, year and death are loaded as x-axis, y-axis and z-axis respectively with exposure as the offset parameter. These parameters are internally fitted in Mortality2Dsmooth function available in MortalitySmooth package in smoothing the data. Step3: plot the smoothened data based on user input Method Name PlotHMDDataset Description Plots the smoothened object with the respective axis, legend, axis scale details are automatics customized based on user inputs. Implementation PlotHMDDataset (Xaxis,YAxis,MainDesc,Xlab,Ylab,legend.loc,legend.Val,Plot.Type,Ylim) Arguments Xaxis Vector for plotting X axis value. Here the value would be Age or Year based on user request. Yaxis Vector for plotting X axis value. Here the value would be Smoothened log mortality vales filtered for a particular Age or Year. MainDesc Main details describing about the plot. Xlab X axis label. Ylab Y axis label. legend.loc A customized location of legend. It can take values topright,topleft legend.Val A customized legend description details it can take vector values of type string. Val,Plot.Type An optional value to change plot type. Here default value is equal to default value set in the plot. If value =1, then figure with line is plotted Ylim An optional value to set the height of the Y axis, by default takes max value of vector Y values. Details The generic method PlotHMDDataset in Programs/Graduation_Methods.r plots the smoothened fitted mortality values with an option to customize based on user inputs. The generic method DrawlineHMDDataset in Programs/Graduation_Methods.r plots the line. Usually called after PlotHMDDataset method. 3.5 Graphical representation of smoothed mortality data. In this section we shall look into graphical representation of mortality data for selected countries Scotland and Sweden. The generic program discussed in previous section 3.4 is used to implement the plot based on customized user inputs. Log mortality of smoothed data v.s actual fit for Sweden. Figure 3.3 Left panel: Plot of Year v.s log(Mortality) for Sweden based on age 40 and year from 1945 to 2005. The points represent real data and red and blue curves represent smoothed fitted curves for BIC and Lamda =10000 respectively. Right panel: Plot of Age v.s log(Mortality) for Sweden based on year 1995 and age from 30 to 90. The points represent real data red and blue curves represent smoothed fitted curves for BIC and Lamda =10000 respectively. Log mortality of smoothed data v.s actual fit for Scotland Figure 3.4 Left panel: Plot of Year v.s log(Mortality) for Scotland based on age 40 and year from 1945 to 2005. The points represent real data and red and blue curves represent smoothed fitted curves for BIC and Lamda =10000 respectively. Right panel: Plot of Age v.s log(Mortality) for Scotland based on year 1995 and age from 30 to 90. The points represent real data red and blue curves represent smoothed fitted curves for BIC and Lamda =10000 respectively. Log mortality of Females Vs Males for Sweden The Figure 3.5 given below represents the mortality rate for males and females in Sweden for age wise and year wise. 3.5 Left panel reveals that the mortality of male is more than the female over the years and has been a sudden increase of male mortality from mid 1960s till late 1970s for male The life expectancy for Sweden male in 1960 is 71.24 vs 74.92 for women and it had been increasing for women to 77.06 and just 72.2 for male in the next decade which explains the trend. Figure 3.5 Left panel: Plot of Year v.s log(Mortality) for Sweden based on age 40 and year from 1945 to 2005. The red and blue points represent real data for males and females respectively and red and blue curves represent smoothed fitted curves for BIC males and females respectively. Right panel: Plot of Age v.s log(Mortality) for Sweden based on year 2000 and age from 25 to 90. The red and blue points represent real data for males and females respectively and red and blue curves represent smoothed fitted curves for BIC males and females respectively. The Figure 3.5 represents the mortality rate for males and females in Sweden for age wise and year wise. 3.5 Left panel reveals that the mortality of male is more than the female over the years and has been a sudden increase of male mortality from mid 1960s till late 1970s for male The life expectancy for Sweden male in 1960 is 71.24 vs 74.92 for women and it had been increasing for women to 77.06 and just 72.2 for male in the next decade which explains the trend. (https://www.scb.se/Pages/TableAndChart____26041.aspx) The 3.5 Right panel shows the male mortality is more than the female mortality for the year 1995, The sex ratio for male to female is 1.06 at birth and has been consistently decreasing to 1.03 during 15-64 and .79 over 65 and above clearly explaining the trend for Sweden mortality rate increase in males is more than in females. (https://www.indexmundi.com/sweden/sex_ratio.html) Log mortality of Females Vs Males for Scotland Figure 3.6 Left panel: Plot of Year v.s log(Mortality) for Scotland based on age 40 and year from 1945 to 2005. The red and blue points represent real data for males and females respectively and red and blue curves represent smoothed fitted curves for BIC males and females respectively. Right panel: Plot of Age v.s log(Mortality) for Scotland based on year 2000 and age from 25 to 90. The red and blue points represent real data for males and females respectively and red and blue curves represent smoothed fitted curves for BIC males and females respectively. The figure 3.6 Left panel describes consistent dip in mortality rates but there has been a steady increase in mortality rates of male over female for a long period starting mid 1950s and has been steadily increasing for people of age 40 years.The 3.6 Right panel shows the male mortality is more than the female mortality for the year 1995, The sex ratio for male to female is 1.04 at birth and has been consistently decreasing to .94 during 15-64 and .88 over 65 and above clearly explaining the trend for Scotland mortality rate increase in males is more than in females. https://en.wikipedia.org/wiki/Demography_of_Scotland . Log mortality of Scotland Vs Sweden Figure 3.7 Left panel:- Plot of Year v.s log(Mortality) for countries Sweden and Scotland based on age 40 and year from 1945 to 2005. The red and blue points represent real data for Sweden and Scotland respectively and red and blue curves represent smoothed fitted curves for BIC Sweden and Scotland respectively. Right panel:- Plot of Year v.s log(Mortality) for countries Sweden and Scotland based on year 2000 and age from 25 to 90. The red and blue points represent real data for Sweden and Scotland respectively and red and blue curves represent smoothed fitted curves for BIC Sweden and Scotland respectively. The figure 3.7 Left Panel shows that the mortality rates for Scotland are more than Sweden and there has been consistent decrease in mortality rates for Sweden beginning mid 1970s where as Scotland mortality rates though decreased for a period started to show upward trend, this could be attributed due to change in living conditions. Chapter 4 Pricing Life insurance products using mortality rates In the previous chapter 3 we discussed the methodology used in constructing mortality rates from Human Mortality Database and smoothing them using MortalitySmooth package. The smoothed graduated data is then used in life insurance companies to estimate pricing in insurance products like annuity and life insurance. Decline in mortality in general has posed one of the key challenges to actuaries in planning, estimating and designing public retirement and life annuities for smooth functioning of the business. Also, calculation of optimal expected present values required in pricing and reserving of long-term benefits depends on projected mortality values. This process eliminates the scope of future insolvency situations and safeguards from wrong projection of future cost. Therefore, actuaries use lifetables to analyse risk and estimate them efficiently. In this chapter we shall discuss about different methods involved in constructing lifetables and commutation functions using mortality rates. These computed values are used to price different insurance products like annuity, term annuity, deferred annuity, life insurance, term insurance, deferred insurance and so on. 4.1 Life insurance systems and commutation functions In this section we shall briefly describe some of the basic insurance products used in insurance industry and state the respective commutation functions. In view of the fact that, most calculations involves computation of expected present values for death benefits paid to the insurer or periodic annuity payments until death of the policy holder. Thus we define basic notations as follows discounted value for x years, where interest rate i is assumed to be .04 and Expected number of survivors at aged x. We can assume to be 100000 Expected number of deaths between x and x + 1. and and and 4.2 Life annuity Whole life annuity payable in advance Payment of 1 made at the beginning of each year while the policy taken at age x by the policy holder is alive. Whole life annuity payable in arrears Payment of 1 made at the end of each year while the policy taken at age x by the policy holder is alive. = Whole life annuity payable continuously Payment of 1 made at the end of each year while the policy taken at age x by the policy holder is alive. n year Temporary annuity payable in advance Payment of 1 made at the beginning of each year while the policy taken at age x by the policy holder is alive for a maximum of n years. n-year Deferred annuity payable in advance Payment of 1 made at the beginning of each year while the policy taken at age x by the policy holder is alive. The first payment is made to the policy holder at age x + n. The commutation function is given as follows Increasing annuity Immediate annuity due paying 1 now, 2 in next year and so on provided the policy holder is alive when the payment is due. The commutation function is defined as follows. 4.3 Life insurance Whole life insurance Death benefit of 1 payable at end of year of death of a policy holder currently aged x for death occurring anytime in near future. n-year Term insurance Death benefit of 1 payable at end of year of death of a policy holder currently aged x for death occurring within n years. n-year Pure Endowment Benefit of 1 payable at end of n years of period provided the policy holder is still alive. n-year Endowment Benefit of 1 payable immediately on the death of policy holder within n years or at the end of n years if policy holder is still alive at age x + n. This shows it is the sum of n-year term insurance and n-year pure endowment as follows. Increasing Whole life insurance Benefit payable at end of the year of death of the policy holder where the amount of payment is k+1 if policy holder dies between age x+k and x+k+1. The commutation function is defined as follows. 4.4 R program implementation In this section we shall explain the different steps applied to price insurance products. 4.4.1 Construct lifetables and commutation functions. The smoothed mortality data is used to compute other lifetables values such as ,, etc. These vector values are in turn used to construct commutation functions variable values such as , , , , . Finally, Annuity and life insurance products are calculated, plotted and tabulated. CalculateCommFunctions Method Name CalculateCommFunctions Description Construct life table values and commutation function values and returns a list of commutation function variables using as input values. Implementation CalculateCommFunctions (mux) Arguments mux Vector value of smoothened data. Details The function CalculateCommFunctions is used to return computed commutation function values. The is assumed as 100000 and values of is used to compute . These values are looped to calculate respective commutation function variables and returned as a list. Computation and graphical representation of Life insurance products Whole life annuity Method Name ComputeAnnuity.Life Description Returns vector value containing computed annuity life payable in advance. The interest rate is assumed at 4% Implementation ComputeAnnuity.Life (index,CommFunc) Arguments index length of the annuity vector. CommFunc list containing the required values of commutation variable required to compute annuity values. Details The function Calculates life annuity using, vector as input values in the CommFunc parameter as list. Figure 4.1 Plot of age v.s annuity prices for males and females based on year 2000 and age from 20 to 90. The red and blue curves represent smoothed fitted curves for males and females respectively. The Left panel represents plot for Sweden and right panel represents plot for Scotland. From figure 4.1 we infer that annuity prices for males and females in Scotland are more expensive than males and females in Sweden, It is because the mortality rates of Sweden is lesser than mortality rates of Scotland as discussed in Section 3.5. Also In general Males annuity prices are more expensive than females in each country because mortality rates of males are more than the females as discussed in Section 3.5. ComputeWholeInsurance.Life Method Name ComputeWholeInsurance.Life Description Returns vector value containing computed whole insurance life. Implementation ComputeWholeInsurance.Life (index,CommFunc) Arguments index length of the annuity vector. CommFunc list containing the required values of commutation variable required to compute whole insurance values. Details The function calculates whole life insurance using, vector values as mentioned above in previous section. Figure 4.2 Plot of age v.s Whole life insurance prices for males and females based on year 2000 and age from 20 to 90. The red and blue curves represent smoothed fitted curves for males and females respectively. The Left panel represents plot for Sweden and right panel represents plot for Scotland. From figure 4.2 we infer that whole life insurance prices increases as age increases and based on the y axis scales we can infer that Scotland whole life insurance prices are more than the Sweden. In general, females whole life insurance are less expensive than males due to lesser mortality rates as discussed in Section 3.5. Compute Increasing WholeInsurance.Life Method Name ComputeIncreasingWholeInsurance.Life Description Returns vector value containing computed increasing whole insurance life. Implementation ComputeIncreasingWholeInsurance.Life (index,CommFunc) Arguments Index length of the annuity vector. CommFunc list containing the required values of commutation variable required to compute whole insurance values. Details The function calculates whole life insurance using, vector values as mentioned above in previous section. Figure 4.3 Plot of age v.s Increasing Whole life insurance prices for males and females based on year 2000 and age from 20 to 90. The red and blue curves represent smoothed fitted curves for males and females respectively. The Left panel represents plot for Sweden and right panel represents plot for Scotland. From figure 4.3 we infer that whole life insurance prices increases as age increases until 60 and decrease rapidly till age reaches 90 and based on the y axis scales we can infer that Scotland whole life insurance prices are more than the Sweden. In general, females increasing whole life insurance are less expensive than males but converges as age appoaches to 90 this is due to lesser mortality rates as discussed in Section 3.5. Compute Increasing Annuity.Life Method Name ComputeIncreasingAnnuity.Life Description Returns vector value containing computed increasing annuity life. The interest rate is assumed at 4% Implementation ComputeIncreasingAnnuity.Life (index,CommFunc) Arguments Index length of the annuity vector. CommFunc list containing the required values of commutation variable required to compute whole insurance values. Details The function calculates whole life insurance using, vector values as mentioned above in previous section. Figure 4.4 Plot of age v.s Increasing Whole life insurance prices for males and females based on year 2000 and age from 20 to 90. The red and blue curves represent smoothed fitted curves for males and females respectively. The Left panel represents plot for Sweden and right panel represents plot for Scotland. From figure 4.4 we infer that increasing Annuity prices decreases as age increases Also, Scotland increasing Annuity prices are slightly more than the Sweden. In general, females increasing Annuity prices are less expensive than males but converges as age approaches to 90. Conclusions In this dissertation, we set out to show how R packages such as actuar,Mortalitysmooth,MASS can be used to implement aggregate loss claims and human mortality. We used compound distribution to model aggregate claims using actuar and P-splines smoothing techniques to smooth mortality data using Mortalitysmooth package. We finally explained these concepts using real time data such as Danish data and Human Mortality database for Scotland and Sweden and priced life insurance products respectively. In chapter 2 we presented general background to compound distribution in modelling aggregate claim and performed simulation using compound Poisson distribution. Our analysis suggested that Weibull fits the loss claim distribution well using goodness of test fit. Finally we analysed Danish loss insurance data from 1980 to 1990 and used Negative binomial distribution for number of claims and simulated for 1000 samples using Gamma distribution and concluded that Gamma distribution gave a better fit using histogram and chi-square goodness of test fit. In chapter 3 we explained briefly on concepts of graduation, generalised linear models. The smoothening techniques using P-splines were presented and the smoothing parameter was calculated using Bayesian information criterion techniques. We obtained deaths and exposure data from Human Mortality Database for selected countries Sweden and Scotland and implemented mortality rates smoothing using mortalitysmooth package under R. Necessary graphs representing actual data, smoothed mortality data using Bayesian information criteria and smoothing parameter =10000 were presented for the selected countries. We also compared the mortality rates based on various sets such as Males and females for specific country or total mortality rates across countries like Sweden and Scotland for a given time frame ranging age wise or year wise. We finally concluded that mortality rates for Scotland are more than Sweden and in general the mortality rates for males are more than the females. In chapter 4 we looked into various life insurance and pension related products widely used in the insurance industry and constructed life tables and commutation functions to implement annuity values using the smoothed data derived using the methods discussed in chapter 3. We compared and plotted for some of the insurance products and concluded that whole life annuity price decrease as age increases and males annuity prices are more than the females.