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).