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The Estimation of the Parameters of a Negative Binomial Distribution with Special Reference to Psychological Data

Published online by Cambridge University Press:  01 January 2025

Herbert S. Sichel
Herbert S. Sichel*
Affiliation:
National Institute for Personnel Research, South African Council for Scientific and Industrial Research
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Abstract

As an analytical tool the negative binomial distribution may have wide applications in the psychological field. The estimation of its parameters is demonstrated to be often inefficient when fitting by the method of moments. This causes possibly true hypotheses to be rejected. Formulas for the efficiency of the moment method and solution of the likelihood equations are derived. Efficiency graphs and detailed tables for the \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\lambda (r,\hat p)$$\end{document} function reduce the maximum-likelihood method to a minimum of computational labour. Practical applications of the ease and power of the M.L. procedure are given.

Type
Original Paper
Information
Psychometrika , Volume 16 , Issue 1 , March 1951 , pp. 107 - 127
Copyright
Copyright © 1951 The Psychometric Society

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Footnotes

*

The author wishes to express his gratitude to the South African Council for Scientific and Industrial Research for permission to publish this paper; to Mr. A. G. Arbous for supplying the data on absenteeism; to Mr. R. V. Sutton for the data on Two-hand Co-ordination errors; and last, but not least, to the staff of the Statistical Section who computed various tables under the expert guidance of Mr. J. S. Maritz.

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