Date of Award

5-1950

Degree Type

Master's Essay - Restricted

Degree Name

Master of Science (MS)

Department

Mathematical and Statistical Sciences

First Advisor

Joseph V. Talacko

Second Advisor

H.P. Pettit

Abstract

The technique of moment-generating and characteristic functions plays a powerful role in present-day statistical theory. The method of moments gives satisfactory results in the analysis of frequency distributions and although it could be used directly for the study of probability functions, the moment-generating function is favored by modern statisticians since with it we can define all the moments in one relationship, usually in the form of an infinite series. The characteristic function has gained much favor in recent years. Not only does it define the moments in one relationship as does the moment-generating function, but also, It gives us other important Information concerning the distribution under analysis. We are, however, very often confronted with complicated and Involved expressions for the moment-generating and characteristic functions of various probability functions. Very often it is only after a great deal of labor that one is even able to find a general term for these expressions. It is thus very advantageous if we can express the above generating functions In a simple analytical form, although of course, this is often Impossible.

The Perks function is well known in the graduation of the life tables. The curve has been applied to many types of quantitative growth. It has been discovered that some special forms of the Perks function satisfy the conditions for a probability function. The principle aim of this thesis is to examine the general properties of these probability functions and to discover, if possible, simple analytical forms for their moment-generating functions and characteristic functions, heretofore unpublished.

Comments

A thesis submitted to the Faculty of the Graduate School, Marquette University in Partial Fulfillment of the Requirements for the Degree of Master of Science, Milwaukee, Wisconsin

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