Hostname: page-component-848d4c4894-nmvwc Total loading time: 0 Render date: 2024-06-16T18:37:41.458Z Has data issue: false hasContentIssue false

A Correction for an Underdispersed Event Count Probability Distribution

Published online by Cambridge University Press:  04 January 2017

Extract

We demonstrate that the expected value and variance commonly given for a well-known probability distribution are incorrect. We also provide corrected versions and report changes in a computer program to account for the known practical uses of this distribution.

The probability distribution in question, named the continuous parameter binomial (CPB) by King (1989a), has been known for at least six decades. The publications that reported the moments incorrectly, or were at least unclear about them, include a dated article (Guldberg 1931), a dissertation and several resulting published articles (Katz 1945, 1965), a popular reference book (Johnson and Kotz 1969),' work in political science on event count regression models (King 1989a), and extensions of these event count models in econometrics (Winkelmann and Zimmermann 1991). Event count regression models have become increasingly common in empirical political science research; some recent examples include Wang et al. (1993) and Krause (1994).

Type
Research Article
Copyright
Copyright © Society for Political Methodology 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramowitz, M., and Stegun, I., eds. 1965. Handbook of Mathematical Functions. New York: Dover.Google Scholar
Guldberg, Alf. 1931. “On Discontinuous Frequency-Functions and Statistical Series.” Skandinavisk Aktvarietionskrift 14: 167–97.Google Scholar
Graham, Ronald L., Knuth, Donald E., and Patashnik, Oren. 1989. Concrete Mathematics: A Foundation for Computer Science. Reading: Addison-Wesley.Google Scholar
Johnson, Norman L., and Kotz, Samuel. 1969. Distributions in Statistics: Discrete Distributions. New York: Wiley.Google Scholar
Katz, Leo. 1965. “Unified Treatment of a Broad Class of Discrete Probability Distributions.” In Patil, Ganapati P., ed., Classical and Contagious Discrete Distributions. Calcutta: Statistical Publishing Society.Google Scholar
Katz, Leo. 1945. “Characteristics of Frequency Functions Defined by First Order Difference Equations.” Ph.D. diss. University of Michigan.Google Scholar
King, Gary. 1989a. “Variance Specification in Event Count Models: From Restrictive Assumptions to a Generalized Estimator.” American Journal of Political Science 33: 762784.Google Scholar
King, Gary. 1989b. Unifying Political Methodology: The Likelihood Theory of Statistical Inference. New York: Cambridge University Press.Google Scholar
Krause, George A. 1994. “Federal Reserve Policy Decision Making: Political and Bureaucratic Influences.” American Journal of Political Science 38: 124–44.Google Scholar
Wang, T. Y., Dixon, William J., Muller, Edward N., and Seligson, Mitchell A. 1993. “Inequality and Political Violence Revisited.” American Political Science Review 87: 979–93.Google Scholar
Winkelmann, Rainer, and Zimmermann, Klaus F. 1991. “A New Approach for Modeling Economic Count Data.” Economics Letters 37: 139–43.Google Scholar