Generalized Moment Generating Functions of Random Variables and Their Probability Density Functions

Matthew Chukwuma Michael^1, , Oyeka Cyprain Anene², Ashinze Mpuruoma Akudo¹ and Igabari John Nwabueze³

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

Cite this paper:
Matthew Chukwuma Michael, Oyeka Cyprain Anene, Ashinze Mpuruoma Akudo and 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

Abstract

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.

Keywords:
generalized moments generating functions distribution function arbitrary constant

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