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

A W Kemp

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6 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)2373-2384
Number of pages12
JournalCommunications in Statistics: Theory and Methods
Publication statusPublished - 2001


  • cycles to conception
  • cycle-specific conception rate
  • hazard rate
  • sterility rate
  • beta-geometric distribution
  • waring distribution
  • q-beta mixture
  • q-beta-geometric distribution


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