A form of multivariate gamma distribution
 A. M. Mathal,
 P. G. Moschopoulos
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Let V _{i}, i=1,..., k, be independent gamma random variables with shape αi, scale β, and location parameter γi, and consider the partial sums Z _{1}=V _{1}, Z _{2}=V _{1}+V _{2},..., Z _{k}=V _{1}+...+V _{k}. 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 threeparameter 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.
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 Title
 A form of multivariate gamma distribution
 Journal

Annals of the Institute of Statistical Mathematics
Volume 44, Issue 1 , pp 97106
 Cover Date
 19920301
 DOI
 10.1007/BF00048672
 Print ISSN
 00203157
 Online ISSN
 15729052
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Multivariate gamma model
 cumulative sums
 moments
 cumulants
 multiple correlation
 exact density
 conditional density
 Industry Sectors
 Authors

 A. M. Mathal ^{(1)}
 P. G. Moschopoulos ^{(2)}
 Author Affiliations

 1. Department of Mathematics and Statistics, McGill University, H3A 2K6, Montreal, Canada
 2. Department of Mathematical Sciences, The University of Texas at El Paso, 799680514, El Paso, TX, U.S.A.