Description: This paper discusses a class of asymmetric distributions arising in a random summation scheme. Members of the class are called asymmetric Laplace distributions as the standard Laplace distributions, which are symmetric, constitute a proper subclass. Among distributions which are limits in random summation schemes, asymmetric Laplace distributions play an analogous role to that of normal distributions among distributional limits of non-random sums. Asymmetric LaPlace laws are more 'peaky' and have heavier tails than normal laws. They have stability properties and are convenient in applications, as their densities have explicit forms and estimation procedures are easily implemented. Anticipating increasing interest in this class of distributions, the authors present statistical tools which can be utilized in practice, including algorithms for simulation and estimation. They also discuss more general classes of distributions, where asymmetric Laplace distributions appear as special cases.

Description: The purpose of this paper is to introduce a practical method for interpolation and smoothing and give a number of numerical examples using the method. The method is a variation of the Whittaker-Henderson method. Discussions of this paper are included.

Description: In this paper, methods are presented that allow the systematic graduation of multidimensional data subject to linear constraints. With these constraints the practitioner can impose limitations on the graduation that agree with prior knowledge. Discussions of this paper are included.

Description: This note describes a mortality investigation procedure in which the expected mortality applicable to each new policy for a period of about three years after issue is estimated by use of persistency factors. Discussions of this paper are included.

Description: The method in this paper is to derive expressions for mortality between integral values of age underlying the typical approximations employed, and to compare such expressions. Annuity and life reserve formulas are compared. Discussions of the paper are included.

Description: Recognizing an opportunity to help serve its members in this age of increased financial oversight, the Health Section of the Society of Actuaries commissioned a series of guides on the use of statistical techniques specifically geared for the work of health actuaries. In this first guide in the series, the topic is an estimate well-known to health actuaries- the calculation of incurred but not reported [IBNR] health claims reserves. In particular, this guide focuses on the development of confidence intervals around IBNR estimates.