THE TRUNCATED NEGATIVE BINOMIAL DISTRIBUTION

(1920), Fisher (1941), Haldane (1941), Anscoinbe (1950) and Bliss & Fisher (1953), and is extensively used for the description of data too heterogeneous to be fitted by a Poisson distribution. Observed samples, however, may be truncated, in the sense that the number of individuals falling into the zero class cannot be determined. For example, if chromosome breaks in irradiated tissue can occur only in those cells which are at a particular stage of the mitotic cycle at the time of irradiation, a cell can be demonstrated to have been at that stage only if breaks actually occur. Thus in the distribution of breaks per cell, cells not susceptible to breakage are indistinguishable from susceptible cells in which no breaks occur. Methods for estimation of the parameters of the truncated distribution are considered in this paper. The corresponding problem of estimation of the truncated Poisson distribution has been discussed by David & Johns-on (1952), who also discuss the present problem.