Stochastic comparisons of largest claim amounts from heterogeneous portfolios

Pradip Kundu, Amarjit Kundu and Biplab Hawlader

Statistica Neerlandica, 2023, vol. 77, issue 4, 497-515

Abstract: This paper investigates stochastic comparisons of largest claim amounts of two sets of independent or interdependent portfolios in the sense of some stochastic orders. Let random variable Xi$$ {X}_i $$ (i=1,…,n$$ i=1,\dots, n $$) with distribution function F(x;αi)$$ F\left(x;{\alpha}_i\right) $$, represents the claim amount for ith risk of a portfolio. Here two largest claim amounts are compared considering that the claim variables follow a general semiparametric family of distributions having the property that the survival function F‾(x;α)$$ \overline{F}\left(x;\alpha \right) $$ is increasing in α$$ \alpha $$ or is increasing and convex/concave in α$$ \alpha $$. The results obtained in this paper apply to a large class of well‐known distributions including the family of exponentiated/generalized distributions (e.g., exponentiated exponential, Weibull, gamma and Pareto family), Rayleigh distribution and Marshall–Olkin family of distributions. As a direct consequence of some main theorems, we also obtained the results for scale family of distributions. Several numerical examples are provided to illustrate the results.

Date: 2023
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