Chapman and Hall/CRC
Suitable for statisticians, mathematicians, actuaries, and students interested in the problems of insurance and analysis of lifetimes, Statistical Methods with Applications to Demography and Life Insurance presents contemporary statistical techniques for analyzing life distributions and life insurance problems. It not only contains traditional material but also incorporates new problems and techniques not discussed in existing actuarial literature.
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.
Mathematical statements are carefully and clearly formulated and proved while avoiding excessive technicalities as much as possible. The book illustrates how these statements help solve numerous statistical problems. It also includes more than 70 exercises.
Duration of Life as a Random Variable. Models of Distribution Functions F(x) and Force of Mortality μ(x). The Empirical Distribution Function of Duration of Life. Deviation of Fn(x) from F(x) as a Random Process. Limit of Empirical Process: Brownian Bridge. Distribution of x2 Goodness-of-Fit Statistic. Statistical Consequences of What We Have Learned So Far. Testing Parametric Hypotheses. Unexpected Example — Exponentiality of Durations of Rule of Roman Emperors. Estimation of the Rate of Mortality. Censored Observations. Related Point Processes. Kaplan-Meier Estimator (Product-Limit Estimator) for F. Statistical Inference about F, based on the Kaplan-Meier Estimator. Life Insurance and Net Premiums. More on Net Premiums. Endowments and Annuities. Annuities Certain. Some Problems of General Theory. Right-Tail Behavior of Fn. Non-Parametric Confidence Bounds for Expected Remaining Life. Population Dynamics. Bibliography. Index.