SOURCE:

Faculty: Physical Sciences
Department: Statistics

CONTRIBUTORS:

Matthew C. Michael
Oyeka I. C. A.

ABSTRACT:

This dissertation developed the generalized multivariate moment generating function for some random vectors/matrices and their probability distribution functions with the intention to replace the traditional/conventional moment generating functions due to its simplicity and versatility. The new function was developed for the multivariate gamma family of distributions, the multivariate normal and the dirrichlet distributions as a binomial expansion of the expected value of an exponent of a random vector/matrix about an arbitrarily chosen constant. The function was used to generate moments of random variables and their probability distribution functions; it was applied to data analysis and results obtained were compared with those from existing traditional/conventional methods. It was observed that the function generated same results as the traditional/conventional methods; in addition, it generated both central and non-central moments in the same simple way without requiring further tedious manipulations; it gave more information about the distribution, for instance while the traditional method gives skewness and kurtosis values of 0 and 3 respectively for p-variate multivariate normal distribution, the new methods gives ((0))_(p×1) and 3^p respectively and; it could generate moments of integral and real powers of random vectors/matrices.