Description: This article investigates the properties of the Gompertz distribution function. Explicit formulas for continuous life insurances and annuities are given in terms of the left-truncated gamma function. Moreover, approximations for the mean, variance, skewness and kurtosis of the Gompertz distribution are also given. Finally, the article shows that using a Gompertz assumption at fractional ages produces better a approximation than the usual UDD assumption.

Description: The dependent relationship between two lives is readily analyzed within the context of probability theory. This paper presents useful relationships between certain actuarial and probability functions and then explores measures of dependence. From Transactions of Society of Actuaries 1986, Vol. 38.

Description: Multiple decrement theory traditionally is based on the assumption that competing causes of decrement are stochastically independent even though this assumption is usually not true in reality. This paper presents some fundamental results towards a dependent decrement theory. First, the author shows how to model dependence with copula functions, then he presents a theorem that characterizes the mathematical relationship between the crude and net probabilities when the decrements are dependent, and finally he applies the results by examining the effect of removing cancer from the United States population when cancer is correlated with the other causes of death. From Actuarial Research Clearing House 1994, VOL. 1.

Description: This paper develops the formula for estimation of multivariate copula. These results can be applied to the estimation of correlation coefficients. From the Actuarial Research Clearing House 1994 Vol. 2 .

Description: Summary of the SOA's Annuity Valuation with Dependent Mortality research report which examines the standard industry practice of assuming independent lives for insurance products that cover multiple lives.

Description: This paper presents a new method for blending census and Medicare mortality rates for the U.S. Decennial Life Tables. From the Actuarial Research Clearing House 1992 Vol. 2 .

Description: This paper describes how Markov chain Monte Carlo and related methods recently presented in the statistical literature can be used to quickly and efficiently simulate random draws from distributions with log-concave or nearly log-concave densities. From Transactions of Society of Actuaries 1995, Vol. 47.

Description: Consider a portfolio of insurance policies where the mean frquency of claims for each policy may vary. A reasonable assumption is that the number of claims for a policy is a Poisson random variable. In this paper the author shows how to test this hypothesis under certain conditions. He then presents some nonparametric tests for this and other hypotheses about the risk distribution function. Actuarial Research Clearing House 1992, VOL. 1.

Description: This article discusses a continuous estimator of a mixing distribution. Specifically the estimator investigated is a mixture of gamma distributions whose parameters are calculated by considering the determinants of certain moment matrices. From Actuarial Research Clearing House 1993, VOL. 2.

Description: This paper investigates nonparametric estimators of the distribution function that are based on mixtures of gamma distributions when we have a random sample from a continuous distribution function. From Actuarial Research Clearing House 1993, VOL. 3.