TABLES OF THE LOGARITHMIC SERIES DISTRIBUTION

1. Summary. The paper tabulates individual and cumulative terms of the logarithmic series probability distribution using the mean of the distribution as entry argument. The range of the table is ,u = 1.1 (0.1) 2.0 (0.5) 5.0 (1.0) 10.0. The tables are prefaced by introductory material, outlining the history and applications of the distribution, deducing generating functions and moments, and giving a method of obtaining the terms of logarithmic series distributions outside the range of those tabled. 2. History and applications. The logarithmic series' distribution was first brought to the notice of statisticians by Fisher [3], in connection with work by Corbet on the distribution of butterflies in the Malayan Peninsula, and data by Williams on the number of moths of different species caught in a light-trap in a given period. In connection with the above data, Fisher assumed that for a given species the number of individuals caught in unit time followed a Poisson distribution with parameter X. Because of the unequal abundance of different species, however, different varieties have unequal probabilities of being caught, this variation in risk being represented by different values of X in the Poisson distribution e-XXn/n! (cf. Greenwood and Yule [5]). If X is distributed with a gamma-type probability density function (ck/r(k)) e-CX Xk-1 dX, the relative frequency with which exactly n individuals of a species are captured is given by the coefficient of tn in