Univariate and multivariate mixtures of exponential distributions, with applications in risk modeling

Cossette Helene; Marceau Etienne; Mtalai ItreVeilleux Dery

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Univariate and multivariate mixtures of exponential distributions, with applications in risk modeling

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Mixed exponential distributions are frequently used in actuarial risk modeling. Distributions obtained through mixtures allow greater flexibility in the modeling of nonlife insurance loss amounts. Several research works have studied mixed exponential distributions in univariate and multivariate settings. The present article highlights the usefulness of such distributions and lays the story of the mixing technique behind them. It also explains the underlying link between all these works. We study in detail three univariate and multivariate mixed exponential distributions defined with a discrete mixing random variable (rv). For each of these three univariate (multivariate) mixed exponential distributions and using an appropriate scaling, we identify the continuous mixing rv to which converges in distribution the discrete mixing rv and the corresponding univariate (multivariate) mixed exponential distribution. In a multivariate setting, we show that these three choices of discrete mixing distributions lead us to known Archimedean copulas constructed with continuous mixing rvs. Applications in actuarial science of these distributions are presented throughout the article highlighting their many uses and useful properties.

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《Applied stochastic models in business and industry》 |2021年第4期|675-702|共28页
作者
Cossette Helene; Marceau Etienne; Mtalai ItreVeilleux Dery;
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作者单位

Univ Laval, Ecole Actuariat, Quebec City, PQ, Canada;

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原文格式 PDF
正文语种英语
中图分类应用数学;
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Archimedean copulas; discrete mixing distribution; multivariate mixture of exponential distributions; risk models with dependence;

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Univariate and multivariate mixtures of exponential distributions, with applications in risk modeling

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