A form of multivariate gamma distribution
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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 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.
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- A form of multivariate gamma distribution
Annals of the Institute of Statistical Mathematics
Volume 44, Issue 1 , pp 97-106
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- Multivariate gamma model
- cumulative sums
- multiple correlation
- exact density
- conditional density
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