THE q-BETA-GEOMETRIC DISTRIBUTION AS A MODEL FOR FECUNDABILITY

Abstract

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 − 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 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.

Keywords:

• Cycles to conception
• Cycle-specific conception rate
• Hazard rate
• Sterility rate
• Beta-geometric distribution
• Waring distribution
• q-beta mixture
• q-beta-geometric distribution

ACKNOWLEDGMENT

I would like to thank Professor R. C. Gupta and Professor P. L. Gupta for inviting me to visit them at the University of Maine and for giving me the opportunity to present this material at the International Conference on Statistics in the 21st Century, held at the University of Maine on June 29–July 1, 2000.