Canadian Journal of Statistics

Selecting a power‐series distribution for goodness of fit

Journal Article


The binomial, Poisson, logarithmic, negative binomial, and extended negative binomial distributions are characterized in the class of power‐series distributions (1) through a differential equation based on the ratio of two successive derivatives of the series function, (2) through the ratio of two probabilities associated with two successive values in the range of the random variable, and (3) through the ratio of two consecutive factorial moments. The ratios referred to in (2) and (3) above can be utilized to discriminate between the five power‐series distributions mentioned at the beginning.

Related Topics

Related Publications

Related Content

Site Footer


This website is provided by John Wiley & Sons Limited, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ (Company No: 00641132, VAT No: 376766987)

Published features on are checked for statistical accuracy by a panel from the European Network for Business and Industrial Statistics (ENBIS)   to whom Wiley and express their gratitude. This panel are: Ron Kenett, David Steinberg, Shirley Coleman, Irena Ograjenšek, Fabrizio Ruggeri, Rainer Göb, Philippe Castagliola, Xavier Tort-Martorell, Bart De Ketelaere, Antonio Pievatolo, Martina Vandebroek, Lance Mitchell, Gilbert Saporta, Helmut Waldl and Stelios Psarakis.