المستخلص: |
A model in actuarial applications is a simplified mathematical description of a certain actuarial task. Actuarial models are used by actuaries to form an opinion and recommend a course of action on contingencies relating to uncertain future events. The paper deals with fitting the probability distributions used in actuarial analysis of insurance claim frequency and severity to real loss insurance data. First, the real insurance claims frequency is fitted to discrete probability distributions, which cannot fitted to traditional distributions. Second, we introduce to the new distribution called Discrete Generalized Lindley (DGL) distribution, how to estimate its parameters and test it for fitting claims frequency. Third, We test fitting claims severity to 57 parametric distributions and find the data follows Dagum distribution. Finally, we estimate the mean and the variance for aggregate losses model. The Kolmogorov-Smirnov (k-s) and Anderson-Darling (A-D) tests are considered in testing the statistical hypotheses of fitting distributions.
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