Generalized Moment Generating Functions for Some Continuous Multivariate Probability Distributions

The traditional moment generating functions of random variables and their probability distributions are known to not exist for all and/or at points and, where they exist, serious difficult tedious manipulations needed the evaluation higher central non-central moments. This paper developed generalized multivariate function some vectors/matrices distribution with intention replace traditional/conventional due simplicity versatility. new were gamma family distributions, normal dirrichlet as a binomial expansion expected value an exponent vector/matrix about arbitrarily chosen constant. used generate moments results obtained compared those from existing methods. It was observed that generated same methods; in addition, both simple way without requiring further manipulations; gave more information instance while method gives skewness kurtosis values respectively -variate distribution, methods ((0))p*1 and; could integral real powers vectors/matrices.