engleski

On sums of independent generalized Pareto random variables with applications to insurance and CAT bonds

A longstanding open problem in statistics is: what is the exact distribution of the sum of independent generalized Pareto or Pareto random variables? Here, we derive single integral representations for the exact distribution with the integrand involving the incomplete and complementary incomplete gamma functions. Applications to insurance and catastrophe bonds are described.

Characteristic function ; Generalized Pareto distribution ; Incomplete gamma function.

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