Using standard procedures of demographic methodology, analysts working with mortality data are faced with a choice between large, unwieldy arrays of age-specific rates (or equivalent sets of life table entries), or one or more of a summary measures set, such as life expectancies and standardized rates, which does not retain all of the available information. This dissertation describes the development and preliminary testing of a mathematical model derived from elementary considerations of mortality mechanisms in the life table population. The model as developed postulates a Gompertz specification to account for mortality rates increasing with age among adults. Also, a proportion of the population was posited to be subject to a competing constant risk, to account for the declining mortality rates in early childhood. The motivation for this model is that its parameters, estimated for particular populations via nonlinear regression procedures, might be used as more efficient mortality summaries than those routinely used, without loss of conceptual interpretability. In testing life tables for male and female populations of 47 selected nations during the 1960s, the model was shown to be substantially more efficient for reproducing the original life tables than were any of the traditional measures considered.

Title: Annuity modelling in MTPL Author: Bc. Agáta Eštóková Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. Karolína Kočová Supervisor's e-mail address: kkocova@koop.cz Abstract: This diploma thesis focuses on the possibilities of using generational mortality tables for third party liability insurance, mainly for bodily injured. It describes the construction of generational mortality tables and the creation of RBNS claims reserves. Besides the demonstration of these models, the work analyzes the results of calculating reserves in accordance with generational mortality tables and actual mortality tables of the Czech Republic. An impor- tant element in provision calculating is the simulation of future life expectancy of the insured, i.e. random generation of life expectancy based on generational mortality data. Characteristics of the distribution of reserves are derived from simulations. Furthermore, we compare the results of stochastic and determi- nistic approach of computing the reserves. Keywords: third party liability insurance, RBNS, annuity, generational morta- lity tables.

Submitted by Viviane Lima da Cunha (viviane@biblioteca.ufpb.br) on 2017-06-28T11:50:33Z No. of bitstreams: 1 arquivototal.pdf: 2055386 bytes, checksum: 54b255e3d880369a58d905d38a9ae31b (MD5) / Made available in DSpace on 2017-06-28T11:50:33Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 2055386 bytes, checksum: 54b255e3d880369a58d905d38a9ae31b (MD5) Previous issue date: 2017-02-02 / The increase in life expectancy registered in the last decades in Brazil was one of the most important achievements of society and brought new challenges in several areas of human knowledge. In order to know the future behavior of life expectancy, the goal of this work was to project the mortality of the Brazilian Semi-Arid from 2015 to 2050. The following methodological steps were performed: obtaining the correction factors of the deaths. Construction of complete Mortality Tables, assembling of databases with the age structure of annual mortality rates from 1980 to 2014, application of the Lee-Carter method for projection of mortality levels and patterns. This method combines a demographic model with a time series model. The projected life expectancies for the year 2050 for the Semi-arid States ranged from 78.25 to 83.82 years. It was concluded that the method produced plausible estimates of mortality levels and standards for most of the geographical areas of the Semi-Arid States, whose Mortality Tables produced may constitute important subsidies in the planning of health and welfare actions and in decision making for the populations of the Semiarid. / O aumento da expectativa de vida registrada nas últimas décadas no Brasil foi uma das mais importantes conquistas da sociedade e trouxe novos desafios em diversas áreas do conhecimento humano. Com o intuito de conhecer o comportamento futuro da expectativa de vida, o objetivo deste trabalho consistiu em projetar a mortalidade do Semiárido brasileiro de 2015 a 2050. Os seguintes passos metodológicos foram executados: obtenção dos fatores de correção dos óbitos; construção de Tábuas de Mortalidade completa; montagem dos bancos de dados com a estrutura etária das taxas de mortalidade anual de 1980 a 2014; aplicação do método de Lee-Carter para projeção dos níveis e padrões de mortalidade. Este método combina um modelo demográfico com um modelo de séries temporais. As expectativas de vida projetadas para o ano 2050 para os Estados do Semiárido variaram de 78,25 a 83,82 anos. Concluiu-se que o método produziu estimativas plausíveis dos níveis e padrões de mortalidade para a maioria dos espaços geográficos dos Estados do Semiárido, cujas Tábuas de Mortalidade produzidas podem se constituir em importantes subsídios no planejamento das ações em saúde e previdência e na tomada de decisão para as populações do Semiárido.

Orientador: Angelo Pires do Prado / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Biologia / Made available in DSpace on 2018-08-06T10:11:40Z (GMT). No. of bitstreams: 1 Mendonca_MarcioJoseCardoso_M.pdf: 850186 bytes, checksum: 09191338420633dd986877635f9988ff (MD5) Previous issue date: 2006 / Resumo: Este trabalho foi realizado com o objetivo de avaliar as diferenças no desenvolvimento e taxas de crescimento populacional de Brevipalpus phoenicis (Geijskes) (Acari: Tenuipalpidae) (ácaro da mancha-anular do cafeeiro) em folhas de quatro cultivares de cafeeiro ('Icatu Vermelho¿, 'Apoatã¿, 'Obatã¿ e'Mundo Novo¿), mantidas em câmara climatizada a 25º ± 1ºC, UR 70 ± 10% e fotofase de 14 horas. As folhas foram separadas por cultivar e divididas em aproximadamente 10 arenas, medindo aproximadamente 1,5 cm x 1 cm de área, delimitadas por barreiras de algodão úmido. Fêmeas de B. phoenicis foram colocadas sobre a superfície das folhas (arenas), por um período de 24 horas para obtenção dos ovos. Após este período, as fêmeas foram retiradas, deixando-se apenas um ovo por arena. As arenas foram examinadas diariamente, avaliando-se os seguintes parâmetros: sobrevivência dos ácaros; viabilidade dos ovos; duração de cada estádio de desenvolvimento, número médio e total de ovos por fêmea; períodos de pré-oviposição, oviposição, pós-oviposição e longevidade dos ácaros. O ácaro plano B. phoenicis apresentou diferenças significativas nos tempos de desenvolvimento, período de pré-oviposição, taxa de oviposição e longevidade, para os diferentes cultivares de café estudados. Os menores períodos de desenvolvimento (ovo a adulto) (28,6 dias), pré-oviposição (2,4 dias) e tempo para completar uma geração (T = 35,2 dias) foram observados para a cultivar 'Mundo Novo¿. O maior número de ovos por fêmea fértil (4,7); maiores taxas líquida de reprodução (Ro = 1,92) e intrínseca de incremento natural (rm = 0,016) foram registrados para a cultivar 'Apoatã¿. As cultivares mais favoráveis para a multiplicação de B. phoenicis foram, nesta ordem: 'Apoatã¿, 'Mundo Novo¿ e 'Obatã, baseando-se nas taxas finitas de incremento. 'Icatu Vermelho¿ mostrou-se ser a cultivar menos favorável à multiplicação de B. phoenicis / Abstract: This work was carried out with the objective of evaluating the differences in development and population growth rates for Brevipalpus phoenicis (Geijskes) (Acari: Tenuipalpidae) (coffee ringspot mite) on leaves of four cultivars of coffee ('Icatu Vermelho¿, 'Apoatã¿, 'Obatã¿ and 'Mundo Novo¿), kept in climatic chambers at 25º ± 1ºC, relative humidity of 70 ± 10% and photophase of 14 hours. The leaves were separated according to the cultivar and divided into approximately 10 arenas, with an area of about 1,5 cm x 1 cm, delimited by wet cotton barrier. Females of B. phoenicis were placed on the leaf surfaces (arenas), for a period of 24 hours for obtaining the eggs. After this period, the females were removed, leaving only one egg of B. phoencis on each arena. The arenas were examined daily, evaluating the following parameters: survival of mites; egg viability; duration of each developmental stage; average and total number of eggs per female; duration of the preoviposition, oviposition and postoviposition periods; and adult longevity. The flat mite, B. phoenicis, presented significant differences in the duration of developmental periods, preoviposition periods, oviposition rates and adult longevities, for the different studied coffee cultivars. The shortest developmental periods (eggadult) (28.56 days), preoviposition periods (2.45 days), and generation times (T = 35.19 days) were observed for the cultivar 'Mundo Novo¿. The highest number of eggs laid per fertile females (4.66); the highest net reproductive rates (Ro = 1.92) and intrinsic rates of natural increase (rm = 0.016) were registered for 'Apoatã¿. The most favorable cultivars for the multiplication of B. phoenicis were, in this sequence: 'Apoatã¿, 'Mundo Novo¿ and 'Obatã, based on the finite rates of increase. 'Icatu Vermelho¿ was shown to be the less favorable cultivar for the multiplication of B. phoenicis / Mestrado / Entomologia / Mestre em Parasitologia

Currently in South Africa when an individual is injured due to the acts of another they may claim damages for the losses which they may incur. These can be claimed from a variety of institutions, such as the Road Accident Fund, Workmen's compensation or an individual's private insurance. In all the afore-mentioned cases the calculation of damages are along the same lines, whereby the damages are quantified first, and thereafter reduced to reflect future possibilities that may occur. Traditionally future losses are reduced to reflect the possibility that the claimant may die at an age prior to the loss being incurred. To account for this risk awards for future losses are reduced using standard South African mortality tables. The set of tables currently being used were calculated from the 1985 South African census, and as such encapsulate the mortality of the population at that period. When the tables were calculated no reliable statistics were available for the Black population the result is that the tables currently being used do not contain a sample of the majority of the population. The thesis first examines, in detail, the calculation methods used to arrive at the value for damages to be awarded using the current set of life tables. Thereafter an analysis is conducted looking at differences between racial groups in the country and geographic locations, in order to uncover the mortality differences between groups to confirm or disprove the proposition that the exclusion of the Black population results in lower levels of mortality being reflected in the South African 1984-1986 life tables. This is accompanied by a review of mortality trenps in South African since 1986. Following from the findings of the expected increase in mortality since 1986, alternative life tables shall be used to show what impact these would have on the calculation of damages. Due to the fact that none of the alternatives return satisfactory results, structured settlements shall be reviewed to illustrate how the shortcomings of the lump sum approach can be circumvented, and altogether avoid the problems of out dated life tables being used as a basis for damage calculations. / KMBT_363 / Adobe Acrobat 9.54 Paper Capture Plug-in

We study development of mortality tables from 1950 to present in Czech Republic. Our aim is to look at the 6 basic models, which can be potentially used to describe behavior of dying for people over 60 years. Models that are being investigated vary from generally accepted Gompertz-Makeham model to logistic models of Thatcher and Kannisto. We also introduce Coale-Kisker and Heligman- Pollard model. Our analysis is concentrated mostly on projecting abilities of given models to the highest ages. Especially for women, where data do not show such dispersion as in the case of men, there is a visible trend that can be described better by using logistic models instead of Gompertz-Makeham model, which has a tendency to overestimate the probabilities of dying in higher ages. Keywords: projection of mortality tables, Gompertz-Makeham, logistic models 1

[ES] En la actualidad resulta de gran importancia el análisis de los fenómenos como el crecimiento poblacional y la reducción de la mortalidad por la repercusión económica y social que dichos procesos tienen en el desarrollo de los países. En este sentido las tablas de vida constituyen una herramienta para comprender, a través de las probabilidades de muerte, la esperanza de vida y otros indicadores, la dinámica poblacional. Lee y Carter (1992), plantearon un modelo, cuyo ajuste permite a los analistas obtener una visión dinámica del comportamiento de la mortalidad durante un periodo de análisis. Esta tesis doctoral busca contribuir en la comprensión de los cambios que ha experimentado la población colombiana en cuanto a mortalidad. Para lograrlo se plantearon cuatro objetivos. El primero, construir modelos estocásticos de mortalidad como Lee-Carter para datos de Colombia y hacer un estudio comparativo de dichos modelos para evaluar su coherencia a partir de la calidad de los resultados obtenidos. El segundo, calcular y analizar algunos indicadores relacionados con la mortalidad tales como la mortalidad infantil, la esperanza de vida al nacer, la esperanza de vida a los 65 años, el índice de Gini al nacer y el índice de Gini a los 65 años. El tercero, aplicar gráficos de control para identificar los momentos en el tiempo y los intervalos de edad en los que la probabilidad de muerte observada es sustancialmente diferente de la pauta de mortalidad en el período estudiado. Para esto, los residuos de los modelos seleccionados se vigilaron mediante el gráfico de control multivariado T2 de Hotelling para detectar cambios sustanciales en la mortalidad que no fueron identificados por los modelos. El cuarto, analizar el comportamiento de la mortalidad para los departamentos de Colombia mediante técnicas de análisis multivariado como el análisis de componentes principales, el clúster jerárquico y el fuzzy clúster, para posteriormente identificar grupos de departamentos con comportamientos similares y caracterizarlos mediante los indicadores de mortalidad estudiados. La metodología descrita relacionada con los tres primeros objetivos se aplicó a datos de las tablas de vida abreviadas por sexo para Colombia para el período 1973-2005, utilizando la información disponible en The Latin America Human Mortality Database. Para el análisis de la mortalidad por departamentos se construyeron nuevas tablas de vida abreviadas por sexo con la información de los departamentos para el período 1985-2014, ajustándonos a la información disponible para los departamentos de Colombia en cuanto a defunciones y población. La metodología fue implementada a través del software estadístico libre R, lo que permite la replicabilidad y reproducibilidad de los resultados. / [CA] En l'actualitat resulta de gran importància l'anàlisi dels fenòmens com el creixement poblacional i la reducció de la mortalitat per la repercussió econòmica i social que aquests processos tenen en el desenvolupament dels països. En aquest sentit les taules de vida constitueixen una eina per a comprendre, a través de les probabilitats de mort, l'esperança de vida i altres indicadors, la dinàmica poblacional. Lee i Carter (1992), van plantejar un model, l'ajust del qual permet als analistes obtenir una visió dinàmica del comportament de la mortalitat durant un període d'anàlisi. Aquesta tesi doctoral cerca contribuir en la comprensió dels canvis que ha experimentat la població colombiana quant a mortalitat. Per a aconseguir-ho es van plantejar quatre objectius. El primer, construir models estocàstics de mortalitat com Lee-Carter per a dades de Colòmbia i fer un estudi comparatiu d'aquests models per a avaluar la seua coherència a partir de la qualitat dels resultats obtinguts. El segon, calcular i analitzar alguns indicadors relacionats amb la mortalitat tals com la mortalitat infantil, l'esperança de vida en nàixer, l'esperança de vida als 65 anys, l'índex de Gini en nàixer i l'índex de Gini als 65 anys. El tercer, aplicar gràfics de control per a identificar els moments en el temps i els intervals d'edat en els quals la probabilitat de mort observada és substancialment diferent de la pauta de mortalitat en el període estudiat. Per a això, els residus dels models seleccionats es van vigilar mitjançant el gràfic de control multivariat T2 de Hotelling per a detectar canvis substancials en la mortalitat que no van ser identificats pels models. El quart, analitzar el comportament de la mortalitat per als departaments de Colòmbia mitjançant tècniques d'anàlisi multivariada com l'anàlisi de components principals, el clúster jeràrquic i el fuzzy clúster, per a posteriorment identificar grups de departaments amb comportaments similars i caracteritzar-los mitjançant els indicadors de mortalitat estudiats. La metodologia descrita relacionada amb els tres primers objectius es va aplicar a dades de les taules de vida abreujades per sexe per a Colòmbia per al període 1973-2005, utilitzant la informació disponible en The Latin America Human Mortality Database. Per a l'anàlisi de la mortalitat per departaments es van construir noves taules de vida abreujades per sexe amb la informació dels departaments per al període 1985-2014, ajustant-nos a la informació disponible per als departaments de Colòmbia quant a defuncions i població. La metodologia va ser implementada a través del programari estadístic lliure R, la qual cosa permet la replicabilidad i reproducibilidad dels resultats. / [EN] The analysis of phenomena such as population growth and mortality reduction is currently of great importance because of the economic and social impact that these processes have on the development of countries. In this sense, life tables are a tool for understanding population dynamics through death probabilities, life expectancy and other indicators. Lee and Carter (1992) proposed a model whose adjustment allows analysts to obtain a dynamic view of the behavior of mortality during a period of analysis. This doctoral thesis seeks to contribute to the understanding of the changes experienced by the Colombian population in terms of mortality. To achieve this, four objectives were proposed. The first, to construct stochastic mortality models such as Lee-Carter for Colombian data and to make a comparative study of these models to evaluate their coherence based on the quality of the results obtained. The second is to calculate and analyze some mortality-related indicators such as infant mortality, life expectancy at birth, life expectancy at age 65, the Gini index at birth and the Gini index at age 65. The third is to apply control charts to identify moments in time and age intervals in which the observed probability of death is substantially different from the mortality pattern in the period studied. For this, the residuals of the selected models were monitored using Hotelling's T2 multivariate control chart to detect substantial changes in mortality that were not identified by the models. Fourth, to analyze the behavior of mortality for the departments of Colombia using multivariate analysis techniques such as principal component analysis, hierarchical clustering and fuzzy clustering, in order to subsequently identify groups of departments with similar behavior and characterize them by means of the mortality indicators studied. The methodology described in relation to the first three objectives was applied to data from the abbreviated life tables by sex for Colombia for the period 1973-2005, using the information available in The Latin America Human Mortality Database. For the analysis of mortality by department, new abbreviated life tables by sex were constructed with information from the departments for the period 1985-2014, adjusting to the information available for the departments of Colombia in terms of deaths and population. The methodology was implemented through the free statistical software R, which allows the replicability and reproducibility of the results. / Díaz Rojo, G. (2021). Ajuste y predicción de la mortalidad. Aplicación a Colombia [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/179995