#### Publication Date

5-24-1956

#### Abstract

The purpose of this paper is to exhibit the main properties of Gamma and Beta distributions and show their relation to certain well known distributions.

In chapter II the Gamma and Beta distributions are defined in terms of Gamma and Beta functions. The moments of these distributions are calculated, and the moment generating function and cumulant generating function for the Gamma distribution are obtained. The curves are classified with respect to parameter values and the curves are graphically illustrated in Figures 1, 2, and 3. The exponential distribution, as a special case of interest, is shown to be a Gamma distribution with parameter one.

#### Degree Name

Mathematics

#### Level of Degree

Masters

#### Department Name

Mathematics & Statistics

#### First Committee Member (Chair)

Reuben Hersh

#### Second Committee Member

James Vernon Lewis

#### Third Committee Member

Paul William Healy

#### Language

English

#### Document Type

Thesis

#### Recommended Citation

Rogers, Calvin. "Beta and Gamma distributions." (1956). https://digitalrepository.unm.edu/math_etds/117