Annals of the Institute of Statistical Mathematics

, Volume 44, Issue 1, pp 97–106

A form of multivariate gamma distribution

  • A. M. Mathal
  • P. G. Moschopoulos

DOI: 10.1007/BF00048672

Cite this article as:
Mathal, A.M. & Moschopoulos, P.G. Ann Inst Stat Math (1992) 44: 97. doi:10.1007/BF00048672


Let Vi, i=1,..., k, be independent gamma random variables with shape αi, scale β, and location parameter γi, and consider the partial sums Z1=V1, Z2=V1+V2,..., Zk=V1+...+Vk. When the scale parameters are all equal, each partial sum is again distributed as gamma, and hence the joint distribution of the partial sums may be called a multivariate gamma. This distribution, whose marginals are positively correlated has several interesting properties and has potential applications in stochastic processes and reliability. In this paper we study this distribution as a multivariate extension of the three-parameter gamma and give several properties that relate to ratios and conditional distributions of partial sums. The general density, as well as special cases are considered.

Key words and phrases

Multivariate gamma modelcumulative sumsmomentscumulantsmultiple correlationexact densityconditional density

Copyright information

© The Institute of Statistical Mathematics 1992

Authors and Affiliations

  • A. M. Mathal
    • 1
  • P. G. Moschopoulos
    • 2
  1. 1.Department of Mathematics and StatisticsMcGill UniversityMontrealCanada
  2. 2.Department of Mathematical SciencesThe University of Texas at El PasoEl PasoU.S.A.