Fitting age-specific fertility rates by a flexible generalized skew-normal probability density function

Mixture probability density functions have recently been proposed to describe some fertility patterns characterized by a bimodal shape. These functions are adequate when the fertility pattern is actually bimodal, but appear to be less useful when the shape of age-specific fertility rates is unimodal. A further model is proposed, based on flexible skew-symmetric probability density functions. This model is able to fit symmetric and skew patterns as well as reflect humps observed in some fertility patterns. It is more parsimonious than mixture distributions and more flexible, showing a good fit with several shapes (bimodal or unimodal) of fertility patterns. Empirical evaluation of the proposed model and comparisons with other functions for Italian data, from 1952 to 2003 and US data from 1933 to 2006 are also discussed.