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
A note on Stieltjes integral
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
Durations of rule of Roman emperors
Chronology of reign of Roman emperors from Kienast (1990)
Distributions of Kolmogorov — Smirnov and w2 statistics from a standard Brownian motion
Estimation of the Rate of Mortality
Censored Observations. Related Point Processes
Kaplan-Meier Estimator (Product-Limit Estimator) for F
A note on Wiener stochastic integral
Statistical Inference about F, based on the Kaplan-Meier Estimator
Testing a simple hypothesis.
Testing a parametric hypothesis
Two-sample problem for censored observations
Why (11.9) is correct? — Ito integral
Life Insurance and Net Premiums
Remark on mixtures of distributions
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
Asymptotic form of the excess life distribution
Recurrence formulae for calculation of non-crossing probabilities
Age structure of a population
"… contains several very interesting relevant real historical examples, such as durations of rules of Roman emperors and number of survival data of male population of New Zealand. The book presents a nice, brief, and clear mathematical theory for statistical methods of the lifetime distribution function. … a good text for a one-semester graduate course on survival analysis featuring demography or life insurance. … The mathematical results and skills presented in the book will be also useful for researchers who are interested in survival analysis or reliability."
—Biometrics, December 2013