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Moments of Continuous Bi-Variate Distributions: An Alternative Approach
Science Journal of Applied Mathematics and Statistics
Volume 1, Issue 5, December 2013, Pages: 62-69
Received: Sep. 29, 2013; Published: Nov. 20, 2013
Authors
Oyeka ICA, Department of Statistics, Nnamdi Azikiwe University Awka, Nigeria
Okeh UM, Department of Industrial Mathematics and Applied Statistics, Ebonyi State University Abakaliki, Nigeria
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Abstract
We propose a method of obtaining the moment of some continuous bi-variate distributions with parameters α1 β1 andα2 β2 in finding the nth moment of the variable x^c y^d (c≥0, d≥0) where X and Y are continuous random variables having the joint pdf, f(x,y).Here we find the so called gn(c, d)defined gn(c, d)= E(X^cY^d+λ)^n, 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 gn(c, d) 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 gn(c, d) are the same as results obtained using other methods such as moment generating functions when they exist.
Keywords
Moment Generating Functions, Bivariate Distributions, Continuous Random Variables, Joint Pdf
Oyeka ICA, Okeh UM, Moments of Continuous Bi-Variate Distributions: An Alternative Approach, Science Journal of Applied Mathematics and Statistics. Vol. 1, No. 5, 2013, pp. 62-69. doi: 10.11648/j.sjams.20130105.15
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