Moment bounds of PH distributions with infinite or finite support based on the steepest increase property

Qi Ming He, Gábor Horváth, Illés Horváth, M. Telek

Research output: Contribution to journalArticle

Abstract

The steepest increase property of phase-type (PH) distributions was first proposed in O'Cinneide (1999) and proved in O'Cinneide (1999) and Yao (2002), but since then has received little attention in the research community. In this work we demonstrate that the steepest increase property can be applied for proving previously unknown moment bounds of PH distributions with infinite or finite support. Of special interest are moment bounds free of specific PH representations except the size of the representation. For PH distributions with infinite support, it is shown that such a PH distribution is stochastically smaller than or equal to an Erlang distribution of the same size. For PH distributions with finite support, a class of distributions which was introduced and investigated in Ramaswami and Viswanath (2014), it is shown that the squared coefficient of variation of a PH distribution with finite support is greater than or equal to 1/(m(m + 2)), where m is the size of its PH representation.

Original languageEnglish
Pages (from-to)168-183
Number of pages16
JournalAdvances in Applied Probability
Volume51
Issue number1
DOIs
Publication statusPublished - Mar 1 2019

Keywords

  • finite support
  • infinite support
  • moment bound
  • Phase-type distribution

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics

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