A form of multivariate gamma distribution

Abstract

Multivariate gamma model, cumulative sums, moments, cumulants, multiple correlation, exact density, conditional density,

Parameter Estimation in Multivariate Gamma Distribution

“…This paper introduces a heuristic approach for parameter estimation in k-variate gamma distribution introduced by Mathai and Moschopoulos [9]. The proposed methodology makes use of the marginal distributions instead of directly using the complex structure of the k-variate gamma distribution.…”

“…Mathai and Moschopoulos [9] introduced a new form of multivariate gamma distribution using mutually independent three-parameter gamma variates. Let V 1 , V 2 , ..., V k be mutually independent random variates where V i ∼ Gamma (α i , β, µ i ), i = 1, 2, ..., k. Let Z 1 = V 1 , Z 2 = V 1 + V 2 , ...,Z k = V 1 + V 2 + ... + V k .…”

“…This distribution is especially useful for models in reliability theory and stochastic process. See Mathai and Moschopoulos [9]. In hydrology, it is extensively used in multivariate flood frequency analysis.…”

“…Some important properties of k-variate gamma distribution as discussed in Mathai and Moschopoulos [9] are listed below.…”

“…Parameter estimation in this distribution is a challenging one as it involves many parameters to be estimated simultaneously. In this paper, the form of multivariate gamma distribution proposed by Mathai and Moschopoulos [9] is considered. This form has nice properties in terms of marginal and conditional densities.…”