ABSTRACT
An inflated zero distribution is the result of mixing a discrete distribution in which the random variable may assume the values, 0, 1, 2, . . . , with a degenerate distribution in which the random variable may only be zero. For an example, consider the counts of specified organisms present in blood samples from patients who may have been infected with a certain disease. The population sampled is composed of'' infected'' and ''noninfected'' individuals. The organism count is zero from "noninfected" individuals, whereas it may be 0, 1, 2, ... from infected individuals. When sample observations are made at random from this mixed population without regard for or knowledge of whether a selected individual is infected or not, the observed distribution of organisms exhibits an inflated zero class. Although any discrete distribution may form the basis for an inflated zero distribution, we will limit our consideration in this section to the Poisson and the negative binomial distributions. Many of the results presented in this section are due to or related to previous results of Cohen (1960e, 1966), David and Johnson (1952), Hartley (1958), Muench (1938), Sampford (1955), and Singh (1962, 1963).
