Description: The conventional way to analyze grouped observations on a single variable is to construct histograms or, sometimes, fit a normal distribution. We extend this latter approach by allowing for transformations to near normality.

Description: This paper introduces a conjecture as to a method for estimating how much has to be added to the probability of ruin by n claims to obtain the probability of ultimate ruin. From the Actuarial Research Clearing House 1994 Vol. 2 .

Description: Sooner or later a casualty actuary is confronted by the question, Given a history of paid loss amounts by calendar year, what should reserves be? Often, it is not possible to accurately gather and analyze additional data within the time constraints for the reserving decision. The algebraic reserving method presented in this paper offers one approach to rapidly addressing this problem.

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: All claim reserve systems endeavor to derive estimates of the unpaid portion of claims which have been incurred over a given period of time, making use of information on numbers of claims and amounts paid on claims as of the valuation date. In this paper, a claim reserve system is described. While the system does produce the traditional type of single-point estimates of claim reserves, it also provides the user with frequency distributions of claim reserves

Description: The purpose of this note is to show how certain formulas of life contingencies can be derived almost painlessly under the uniform distribution of deaths assumption.

Description: Presents a theoretical basis for a computerized methodology for estimating biological age - a measure of time to death.

Description: In this paper, we study a survival regression model known as Cox's proportional Hazards model. We assume that the data available are already grouped and develop a minimum distance estimation procedure that is also applicable when the data are also left or right censored. Asymptotic properties of the estimators are established and the numerical implementation of the method based on an iterated reweighted least squares algorithm is discussed.

Description: We apply decision theory to develop a credibility formula that minimizes a loss function that is a linear combination of a squared-error term and a second-derivative term. The squared-error term measures the accuracy of the estimator, while the second-derivative term constrains the estimator to be close to linear.

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 .