Asymptotic tail behavior of phase-type scale mixture distributions

Leonardo Rojas-Nandayapa; Wangyue Xie

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arXiv · 1502.01811

Asymptotic tail behavior of phase-type scale mixture distributions

Leonardo Rojas-Nandayapa·Wangyue Xie

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Abstract

We consider phase-type scale mixture distributions which correspond to distributions of a product of two independent random variables: a phase-type random variable $Y$ and a nonnegative but otherwise arbitrary random variable $S$ called the scaling random variable. We investigate conditions for such a class of distributions to be either light- or heavy-tailed, we explore subexponentiality and determine their maximum domains of attraction. Particular focus is given to phase-type scale mixture distributions where the scaling random variable $S$ has discrete support --- such a class of distributions has been recently used in risk applications to approximate heavy-tailed distributions. Our results are complemented with several examples.

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BibTeX RIS

Leonardo Rojas-Nandayapa, Wangyue Xie. 2015-02-06. Asymptotic tail behavior of phase-type scale mixture distributions. https://arxiv.org/abs/1502.01811

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