Generalized Methods for Generating Moments of Continuous Distribution
We propose a method of obtaining the moment of some continuous bi-variate distributions with parameters 1122,,andαβαβin finding the nth moment of the variable ()0,0cdxycd≥≥where X and Y are continuous random variables having the joint pdf, f(x,y).Here we find the so called (,)ngcddefined ()(,),ncdngcdEXYλ=+the nth moment of expected value of the t distribution of the cth power of X and dth power of Y about the constant λ.These moments are obtained by the use of bi-variate moment generating functions, when they exist. The proposed (,)ngcd is illustrated with some continuous bi-variate 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 (,)ngcd are the same as results obtained using other methods such as moment generating functions when they exist.
