On the distribution of linear combinations of independent Gumbel random variables

Filipe J. Marques, Carlos A. Coelho, Miguel de Carvalho

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

The distribution of linear combinations of independent Gumbel random variables is of great interest for modeling risk and extremes in the most different areas of application. In this paper we develop near-exact approximations for the distribution of linear combination of independent Gumbel random variables based on a shifted generalized near-integer gamma distribution and on the distribution of the difference of two independent generalized integer gamma distributions. These near-exact distributions are computationally appealing and numerical studies confirm their accuracy, as assessed by a proximity measure used in related studies. We illustrate the proposed approximations on applied problems in networks engineering, computational biology, and flood risk management.

Original languageEnglish
Pages (from-to)683-701
Number of pages19
JournalStatistics and Computing
Volume25
Issue number3
DOIs
Publication statusPublished - May 2015

Keywords

  • Generalized integer gamma distribution
  • Generalized near-integer gamma distribution
  • Gumbel distribution
  • Near-exact distribution
  • Phase type distributions
  • Risk

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