Description: The author comments on the article Exposure Formulas Based on the Assumption of Uniform Distribution of Deaths written by T.N.E. Greville.

Description: This paper introduces density estimation for functions of observations. The nonparametric density estimates are introduced and certain computational issues are discussed and a central limit theorem for the estimator is provided. From Actuarial Research Clearing House 1993, VOL. 1.

Description: This research paper presents a method for smoothing mortality rates using multi-dimensional Whittaker-Henderson Graduation. The paper answers the question: For a given level of fit, how are the smoothness parameters to be chosen so that the graduated rates form, in some natural sense, the smoothest discrete surface?

Description: We find the necessary and sufficient conditions for fitting five given moments by a triatomic distribution. We consider three examples drawn from fire large spread, individual life medium spread and group life small spread insurance data, fit them with triatomics, and compute the ruin probabilities using well known formulas for discrete and for combination of exponentials claim amounts. We then compare our approximations with the exact values that appeared in the literature.

Description: In this paper, Lagrangian distributions are reviewed and some of their properties are studied. Recursive methods are proposed to calculate compound Lagrange distributions. Some examples for a sub-family of Lagrangian Distributions and its compound distributions are studied.

Description: This is the abstract of a paper that presents a model for examining the effect of various relationships between mortality rates and lapse rates on the mortality experience of a cohort of insured lives. It takes an individual approach rather than the aggregate approach used in traditional methods of analyzing selective lapsation. The model assumes that insured lives are healthy at policy issue, but may later move to an impaired state from which the lapse rate is zero. Associated with each insured is an unobservable 'risk level' random variable, which reflects the heterogeneity of the insured group. Individual mortality and lapse rates are functions of the risk level. A numerical illustration provides some interesting results obtained using this model.

Description: Presented at 1983 Actuarial Research Conference. The goal is to estimate the form of distribution of T 'time to an event' given 'z', and to explore the relationship between T and z. The methods outlined can be generalized to problems involving multiple failure times - not restricted to death events.

Description: The Karup-King formula with equal intervals has an elegant symmetric structure providing for efficient calculation. This paper traces the algebra involved in a generalization of this formula to the case of unequal intervals. So far, this formula does not have an elegant structure. However, a degree of elegance can be obtained in terms of matrix notation which can readily be used with a computer language such as APL.

Description: In this paper the authors analyze data from group medical expense insurance claims and show that many insurance loss distributions have very 'heavy tails' because large losses represent a disproportionate fraction of the total cost. They also present a simple model to reproduce and explain the large loss behavior. From Actuarial Research Clearing House 1990, VOL. 2

Description: In this paper, given the three moments of the claim amount, the authors find the di-atomic and the di-exponential distributions that fit the given three moments. They use ruin probability formulas when the claim amount is discete or is a combination of exponentials to compute ruin probabilities based on the claim amount distribution which match the first three moments of the original claim amount distribution. Actuarial Research Clearing House 1992 VOL. 1