A Relation between the Logarithmic, Poisson, and Negative Binomial Series
M. H. Quenouille · Biometrics · 1949
TN RECENT YEARS, many applications [3, 41 have been found for the I logarithmic series developed by R. A. Fisher [11 in an investigation of the frequency distribution of numbers of species of animals obtained in random samples. Fisher derived this distribution by first considering .a Poisson distribution with mean m, since this is the usually observed distribution where we are dealing with homogeneous material. However, where we are dealing with heterogeneous material, it is no longer possibleto assume that m is fixed for all samples, so that Fisher assumed that it was distributed as a Gamma-type variable in the form