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Asymptotic tail behaviour of phase-type scale mixture distributions

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  • Rojas-Nandayapa, Leonardo
  • Xie, Wangyue

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.

Suggested Citation

  • Rojas-Nandayapa, Leonardo & Xie, Wangyue, 2018. "Asymptotic tail behaviour of phase-type scale mixture distributions," Annals of Actuarial Science, Cambridge University Press, vol. 12(2), pages 412-432, September.
    • Handle: RePEc:cup:anacsi:v:12:y:2018:i:02:p:412-432_00
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    Cited by:

    1. Yiqing Chen & Jiajun Liu & Yang Yang, 2023. "Ruin under Light-Tailed or Moderately Heavy-Tailed Insurance Risks Interplayed with Financial Risks," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-26, March.

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