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: 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: The purpose of this paper is to present a parsimonious parametric model that explains the pattern of mortality for select and ultimate mortality tables. Specifically, the author modeled the combined rates found in the 1965-70 ALB Basic Tables. From Actuarial Research Clearing House 1994, VOL. 1.

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: This paper discusses a mixed lognormal estimator of a risk distribution. Using the observed claim frequencies of a portfolio, the author presents a continuous nonparametric estimator of the risk distribution that reproduces some of the empirical moments and converges uniformly. The estimator that is investigated is a mixture of log-normal distributions whose parameters are calculated by considering the determinants of certain moment matrices. From Actuarial Research Clearing House 1993, VOL. 1.

Description: Develops a statistical procedure to fit bivariate distributions of claims in presence of covariates, which allows for a more accurate study of insureds' choice and size in the frequency and severity of the two types of claims.

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.