Statistical methods with applications to demography and life insurance /
Estáte V. Khmaladze.
- xiii, 228 pages : illustrations ; 24 cm
Rev. and expanded version of the Russian ed.
Includes bibliographical references and index.
1 Duration of life as a random variable -- 2 Models of distribution functions F(x) and force of mortality u(x) -- 3 The empirical distribution function of duration of life -- 4 Deviation of Fn(x) from F(x) as a random process -- 5 Limit of empirical process: Brownian bridge. Distribution of x2 goodness of fit statistic -- 6 Statistical consequences of what we have learned so far. Two-sample problems -- 7 Testing parametric hypotheses. Unexpected example -- ex-ponentiality of durations of rule of Roman emperors -- 8 Estimation of the rate of mortality -- 9 Censored observations. Related point processes -- 10 Kaplan-Meier estimator (product-limit estimator) for F -- 11 Statistical inference about F, based on the Kaplan-Meier estimator -- 12 Life insurance and net premiums -- 13 More on net premiums. Endowments and annuities -- 14 Annuities certain. Some problems of general theory -- 15 Right-tail behavior of Fn. Non-parametric confidence bounds for expected remaining life -- 16 Population dynamics.
"The book mainly focuses on the analysis of an individual life and describes statistical methods based on empirical and related processes. Coverage ranges from analyzing the tails of distributions of lifetimes to modeling population dynamics with migrations. To help readers understand the technical points, the text covers topics such as the Stieltjes, Wiener, and Itô integrals. It also introduces other themes of interest in demography, including mixtures of distributions, analysis of longevity and extreme value theory, and the age structure of a population. In addition, the author discusses net premiums for various insurance policies." -- Provided by publisher.