THE POPULATION FREQUENCIES OF SPECIES AND THE ESTIMATION OF POPULATION PARAMETERS

Abstract

A random sample is drawn from a population of animals of various species. (The theory may also be applied to studies of literary vocabulary, for example.) If a particular species is represented r times in the sample of size N, then r/N is not a good estimate of the population frequency, p, when r is small. Methods are given for estimating p, assuming virtually nothing about the underlying population. The estimates are expressed in terms of smoothed values of the numbers nr (r= 1, 2, 3, ...), where nr is the number of distinct species that are each represented r times in the sample. (nr may be described as ‘the frequency of the frequency r’.) Turing is acknowledged for the most interesting formula in this part of the work. An estimate of the proportion of the population represented by the s