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# B. The Beta-Geometric Distribution

DOI link for B. The Beta-Geometric Distribution

B. The Beta-Geometric Distribution book

# B. The Beta-Geometric Distribution

DOI link for B. The Beta-Geometric Distribution

B. The Beta-Geometric Distribution book

## 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.