ABSTRACT

In this case also the parameter p of the geometric distribution may not be assumed to remain constant throughout the course of col­ lecting the data. For example, in human reproduction the random variable Y may be the number of menstrual cycles required for con­ ception in which the parameter p may be interpreted as the pre-cycle conception probability or a measure of fecundability (see Weinberg and Gladen (1986)). We assume that the parameter p is fixed for a given couple, but across couples it varies according to some un­ specified underlying distribution which we assume to be beta with probability density function given by (1.1). Then, the marginal dis­ tribution of Y is

This distribution is known as the beta-geometric distribution. In the human reproduction literature P r(F = y) is the probability that conception occurs at y for a randomly selected couple. As in the case of beta-binomial distribution, the beta-geometric distribution also can be written in terms of the parameter 7r = a / (a + ff) and 0 = 1 /(a + 0), where p is interpreted as the mean parameter and 9 as the shape parameter (see Weinberg and Gladen (1986) for more details), which is given in what follows.