Asymptotic tail behavior of phase-type scale mixture distributions

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.

18 pages, 0 figure

References in corpus (4)

• Asymptotics of Random Contractions
• Asymptotics of supremum distribution of a Gaussian process over a Weibullian time
• On the accuracy of phase-type approximations of heavy-tailed risk models
• Corrected phase-type approximations of heavy-tailed risk models using perturbation analysis

Cited by in corpus (1)

• Approximation of Ruin Probabilities via Erlangized Scale Mixtures