THE q-BETA-GEOMETRIC DISTRIBUTION AS A MODEL FOR FECUNDABILITY
Adrienne W. Kemp · Communication in Statistics- Theory and Methods · 2001
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 Rx = (1 − ρ)/(1 − m x−1 ρ/u), instead of μ/(1 − θ + θx). The set of parameter restraints (0 < m < 1, 0< ρ < 1, 1 < u) is appropriate for retrospective data, whilst the alternative set of restraints (1 < m, 1 < ρ, 0 < u < 1) is appropriate for prospective data. The decrease in Rx 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.