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Asymptotic tail behaviour of phase-type scale mixture distributions

Published online by Cambridge University Press:  29 August 2017

Leonardo Rojas-Nandayapa
Affiliation:
School of Mathematics and Physics, The University of Queensland, Brisbane, QLD 4072, Australia
Wangyue Xie*
Affiliation:
School of Mathematics and Physics, The University of Queensland, Brisbane, QLD 4072, Australia
*
*Correspondence to: Wangyue Xie, School of Mathematics and Physics, The University of Queensland, St Lucia, Brisbane, QLD 4072, Australia. Tel: +61 424494412; E-mail: w.xie1@uq.edu.au

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 non-negative 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.

Type
Paper
Copyright
© Institute and Faculty of Actuaries 2017 

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