Abstract
Conventional parametric count distributions, namely the Poisson and Negative-Binomialmodels, do not offer satisfactory descriptions of empirical distributions of completed cohortparity. One reason is that they cannot model variance-to-mean ratios below unity, that is,underdispersion, which is typical of low-fertility parity distributions. Statisticians haverelatively recently revived two generalised count distributions that can model bothoverdispersion and underdispersion, but that have to date not attracted the attention ofdemographers. The objective of this note is to assess the utility of these distributions, theConway-Maxwell-Poisson and Gamma Count models, for the modelling of paritydistributions, using both simulations and maximum-likelihood fitting to empirical data fromthe Human Fertility Database (HFD). The results show that these generalised countdistributions offer a greatly improved fit compared to customary Poisson and Negative-Binomial models in the presence of underdispersion, without loss of performance in thepresence of equi- or overdispersion.
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