Development of procedure to describe frequency distributions involved in statistical theory is discussed. Representation of frequency distributions by first order differential equation is presented. Classification of various types of distributions based on Pearson parameters is analyzed

Falls, L. W.

English

NASA Technical Reports Server

October 1972	 B72-10602 
NASA TECH BRIEF 
Marshall Space Flight Center 
NASA Tech Briefs announce new technology derived from the U.S. space program. They are issued to encourage 
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be directed to the Technology Utilization Office, NASA, Code KT, Washington, D.C. 20546. 
Program for Standard Statistical Distributions 
The problem: 
There are certain statistical distribution functions 
which, for theoretical and practical reasons, occupy a 
central position in statistical theory. Because of the 
many forms assumed by frequency distributions, a 
logical, efficient procedure to describe those of import-
ance would be desirable. 
The solution: 
This program uses two approaches, one theoretical 
and the other empirical. These are presented as three 
options: option A for the theoretical and options B and 
C for the empirical. 
How it's done: 
Program option A is the Pearson system of frequency 
distributions developed by Karl Pearson. Pearson claimed 
that all the different types of frequency distributions 
that arise in practical statistics can be represented by the 
solutions of a first order differential equation: 
dg(x) =	 (x - a) g(x) 
b0
 + b 1 x + b2 X2 4-... 
The classification of the various types of distributions 
is based upon the evaluation of the "Pearson para-
meters." These parameters are a function of the sample 
moments. This part of the program computes central 
and non-central sample moments up to order eight. The 
parameters are computed, and the program chooses the
appropriate Pearson distribution type based upon the 
evaluation of these parameters. Appropriate variances 
and standard deviations of the Pearson parameters also 
are computed. This option also computes and prints 
required sample statistics including sample means, vari-
ances, standard deviations, and the cumulative distri-
bution function. 
Options B and C of the program "fit" the sample 
input with specified known theoretical distributions. 
This is a straightforward approach to the problem. 
Option B includes continuous distributions and option 
C includes discrete distributions. Included in each distri-
bution fit are expected frequencies, expected cumulative 
probability function, estimated parameters, and "good-
ness of fit" tests. 
Notes: 
1. This program is written in FORTRAN V for use on 
the UNIVAC-I 108. 
2. Inquiries concerning this program should be directed 
to:
COSMIC 
112 Barrow Hall 
University of Georgia 
Athens, Georgia 30601 
Reference: MFS-2 1466
Source: L. W. Falls 
Marshall Space Flight Center
(MFS-2 1466) 
Category 09 
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Aeronautics and Space Administration. Neither the United States
	 information contained in this document, or warrants that such use 
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Program for standard statistical distributions

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