1Department of Mathematics and Statistics, School of Applied Sciences, Delta State Polytechnic, Ogwashi-Uku
2Department of Statistics, Faculty of Physical Sciences, Nnamdi Azikiwe University, Awka, Anambra State
3Department of Mathematics, Delta State University, Abraka, Delta State
American Journal of Applied Mathematics and Statistics.
2017,
Vol. 5 No. 2, 49-53
DOI: 10.12691/ajams-5-2-2
Copyright © 2017 Science and Education PublishingCite this paper: Matthew Chukwuma Michael, Oyeka Cyprain Anene, Ashinze Mpuruoma Akudo, Igabari John Nwabueze. Generalized Moment Generating Functions of Random Variables and Their Probability Density Functions.
American Journal of Applied Mathematics and Statistics. 2017; 5(2):49-53. doi: 10.12691/ajams-5-2-2.
Correspondence to: Matthew Chukwuma Michael, Department of Mathematics and Statistics, School of Applied Sciences, Delta State Polytechnic, Ogwashi-Uku. Email:
megawaves4life@yahoo.comAbstract
This paper seeks to develop a generalized method of generating the moments of random variables and their probability distributions. The Generalized Moment Generating Function is developed from the existing theory of moment generating function as the expected value of powers of the exponential constant. The methods were illustrated with the Beta and Gamma Family of Distributions and the Normal Distribution. The methods were found to be able to generate moments of powers of random variables enabling the generation of moments of not only integer powers but also real positive and negative powers. Unlike the traditional moment generating function, the generalized moment generating function has the ability to generate central moments and always exists for all continuous distribution but has not been developed for any discrete distribution.
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