On the distribution of linear combinations of independent Gumbel random variables

TitleOn the distribution of linear combinations of independent Gumbel random variables
Publication TypeJournal Article
Year of Publication2015
AuthorsMarques FJ, Coelho C, de Carvalho M
JournalSTATISTICS AND COMPUTING
Volume{25}
Pagination683-701
Date PublishedMAY
ISSN0960-3174
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.}

DOI10.1007/s11222-014-9453-5