The moment generating function of the distribution of

This paper presents a proposed alternative method of expression of joint distribution of powers of two continuous random variables when both powers are necessarily not whole numbers. Hence, in finding the alternative moment generating function (AMGF) of the joint distribution of some functions of a given random variable, it is not necessary to find and use the joint distribution of these functions, it is sufficient to simply use the joint distribution of the two random variables and hence quicker to use. Unlike the regular moment generating functions, the alternative method of moment generating function is known to always exist for all continuous probability distributions.   Key words: Moment generating function,  QUOTE   distribution, two random variables.