Multivariate gamma distributions-properties and shape estimation

Abstract

A sequence of suitably defined multivariate gamma distributions with decreasing skewness is proved to converge to the respective multivariate normal distribution. Other properties of multivariate gamma distributions are given, and the generation of pseudorandom numbers is presented. Parameter estimation is shown to reduce to the evaluation of shape parameter ? in the univariate case. A new estimator of ?, based on the mode of the smallest sample observation, is proposed. A simulation study suggests that the estimator performs better than several other estimators being in use

Keywords:

• Iterative procedure
• maximum likelihood estimators
• mode
• moment estimators
• positively quadrant dependence
• skewness