The q-beta-geometric distribution as a model for fecundability

The number of sterile couples in a retrospective study of the number of cycles to conception is necessarily zero; this is not so for a prospective study. The paper puts forward a modification of Weinberg and Gladen's beta geometric model for cycles to conception that is suitable for both types of investigation. The probability that a couple achieves conception at the xth cycle, but not earlier, is assumed to take the form R-x = (1 - rho)/(1 - m(x-1) rho /u), instead of mu/(1 - theta + thetax). The set of parameter restraints (0 < m < 1, 0 < rho < 1, 1 < u) is appropriate for retrospective data, whilst the alternative set of restraints (1 < m, 1 < rho, 0 < u < 1) is appropriate for prospective data. The decrease in R-x over time can be interpreted not only as a time effect, but also as a heterogeneity effect by replacing Weinberg and Gladen's beta mixture of geometric distributions by a q-beta mixture.