STATISTICS OF BINOMIAL NUMBER FLUCTUATIONS

When birth terms in the rate equation for a simple birth-death population process are proportional to the difference between the number of individuals present and a larger fixed number, the equilibrium population obeys a binomial distribution. In this paper the statistics of such a process are investigated. Properties of the related counting process, including interval statistics, are calculated and the results used to evaluate the autocorrelation function of a binomial telegraph wave.