Description: During the last decade, a vast activity had been observed in generalizing of the classical discrete distributions. The main idea was to apply the extended versions fur modeling different kinds of dependent count or frequency data structure in various fields. In the present paper we suggest extensions of the classical univariate geometric, negative binomial, Poisson, Bernoulli, binomial and logarithmic series distributions, by including an additional parameter. It has a natural interpretation in terms of zero-inflation, and because of this we named the corresponding generalized versions adding inflated-parameter.

Description: By the use of resampling and extreme value statistics we will develop a method to reduce the time and costs of testing insurance company insolvency. Most ruin models require assumptions about the surplus distribution and/or assumptions about the claims count and severity distributions. The actuary may not be comfortable in making these ruin assumptions. Instead, he or she may generate such distributions by running extensive computer simulations of corporate models, I introduce a method to reduce the number of simulations necessary' to estimate the 1 and 0.1 percentiles of the surplus distribution. This approach 'cuts off' the tail at approximately the tenth percentile of the sample distribution and generates new tails for the distribution by resampling. Averages of the new order statistics approximate the I and 0.1 percentiles.