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

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  • Stefano Mazzuco
  • Bruno Scarpa

Abstract

type="main" xml:id="rssa12053-abs-0001"> 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 they 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 can fit symmetric and skew patterns as well as reflect humps that are 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 model proposed and comparisons with other functions for Italian data from 1952 to 2003 and US data from 1933 to 2006 are also discussed.

Suggested Citation

  • Stefano Mazzuco & Bruno Scarpa, 2015. "Fitting age-specific fertility rates by a flexible generalized skew normal probability density function," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 178(1), pages 187-203, January.
    • Handle: RePEc:bla:jorssa:v:178:y:2015:i:1:p:187-203
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    File URL: http://hdl.handle.net/10.1111/rssa.2014.178.issue-1
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    Cited by:

    1. Natalia Khorunzhina & Jean-François Richard, 2019. "Finite Gaussian Mixture Approximations to Analytically Intractable Density Kernels," Computational Economics, Springer;Society for Computational Economics, vol. 53(3), pages 991-1017, March.
    2. Adelchi Azzalini & Marc G. Genton, 2015. "Discussion," International Statistical Review, International Statistical Institute, vol. 83(2), pages 198-202, August.
    3. M. C. Jones, 2015. "Rejoinder," International Statistical Review, International Statistical Institute, vol. 83(2), pages 223-227, August.
    4. Chao Zhang & Piotr Kokoszka & Alexander Petersen, 2022. "Wasserstein autoregressive models for density time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(1), pages 30-52, January.
    5. Rendao Ye & Bingni Fang & Weixiao Du & Kun Luo & Yiting Lu, 2022. "Bootstrap Tests for the Location Parameter under the Skew-Normal Population with Unknown Scale Parameter and Skewness Parameter," Mathematics, MDPI, vol. 10(6), pages 1-23, March.
    6. Bufalo, Michele & NIGRI, ANDREA, 2024. "Trimodal extension based on the flexible generalized skew-normal distribution," OSF Preprints axu6g, Center for Open Science.

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