The n^th moment of X^cY^d

Oyeka ICA and Okeh UM

Physical Sciences Research International
Published: November 7 2013
Volume 1, Issue 4
Pages 123-132

Abstract

We propose an alternative method of obtaining the nth moment of the joint distribution of the cth power of the random variable X and the dth power of the random variable Y about zero for all non-negative values of c and d. The method, denoted by µ_n (c, d), may be termed ‘moment of power generating function (mpgf)’. It exists for all continuous distributions unlike in contenders-the factorial moments and the moment generating functions which do not always exist. The proposed µ_n (c, d) is illustrated with some continuous bivariate distributions and is shown to be easy to use even when the powers of the random variables being considered are non-negative real numbers that need not be integers. The results obtained using µ_n (c, d) are the same as results obtained using other methods such as moment generating functions when they exist.

Keywords: Moment generating function, joint distribution, integers, probability density function, non-negative real numbers, Skewness, Kurtosis, marginal distribution.

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