Journal of Statistics Applications & Probability

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This article proposes an analytical method to approximate the probability density function (PDF) and the cumulative distribution function (CDF) of the total amount of non-life claims to be paid by the insurer over a financial period considered. The individual claims amounts are independent positive random variables following the generalized gamma distribution (GGD) and distributed in a non-identical manner. The analytical approach suggested relies on the Fox H-function. The Fox H-function has various applications available in the literature. The method developed has demonstrated its performance both in respect of the result obtained (in comparison to the Monte-Carlo method) and in respect of simplicity (easily accessible for the most common claims amount distributions). The resulting PDF expression can be directly used to estimate the technical benefit, total cost, and ruin probability of the non-life insurance company.

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