Date of Award
Master of Science
Master of Mathematics
Since histograms give little quantitative information about distribution, more detail descriptions are desirable. These descriptions are attained by moments of distribution. We will be primarily concerned with the first two moments. The first two moments are associated with the mean and standard deviation of a given distribution. It is to be observed now that the methods used for obtaining the mean and standard deviation of ordinary statistical data will not suffice when applied to known theoretical distributions.
Our purpose here is to consider particular theoretical freqiency distributions as models for empirical distribution.
Chapter one describes essential terminology and definitions used throughout the paper.
Chapter two discusses moments and the moment generating function. It also shows how the moment generating function actually produces moments.
Chapter three is devoted to the application of the moment generating function to the binomial distribution. It also shows that the definitions and the moment generating function produce the same moments.
Chapter four discusses the application of the moment generating function to the Poisson distribution.
Chapter five demonstrates the application of the moment generating function to the normal distribution.
Chapter six shows the application of the moment generating function to the chi-square distributions.
Finally the summary and bibliography are given.
A. D. Steward
Prairie View A&M College
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Date of Digitization
John B Coleman Library
City of Publication
McAfee, O. W. (1959). Application of the Moment Generating Function to Various Other Frequency Functions. Retrieved from https://digitalcommons.pvamu.edu/pvamu-theses/659