Multivariate Lagrange distributions and a subfamiliy

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Abstract

Second order moments about its means, i.e. the variances and covariances for multivariate Lagrange distributions are derived in a matrix form. A subfamily of multivariate Lagrange distributions which can be characterized as the distributions of customers served in a busy period in qnonos with some conditions are considered. Theorems about their probability functions, one of which is a multivariate generalization of a formula by Takàcs(1989), are given and the means and second order moments about its means are considered. As an example, a multivariate Borel-Tanner distribution is derived.

Original languageEnglish
Pages (from-to)2185-2197
Number of pages13
JournalCommunications in Statistics - Theory and Methods
Volume27
Issue number9
DOIs
Publication statusPublished - 1998 Jan 1
Externally publishedYes

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Keywords

  • Busy period
  • Multivariate Borel-Tanner distribution
  • Multivariate Lagrange expansion
  • Second order moments about its means

ASJC Scopus subject areas

  • Statistics and Probability

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