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Trimodal extension based on the flexible generalized skew-normal distribution

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  • Bufalo, Michele
  • NIGRI, ANDREA

Abstract

We propose a novel class of generalized skew-normal densities that improves the flexibility of empirical distributions and can systematically capture skewness, heavy tails, and multimodality. We extend the so-called flexible generalized skewnormal (FGSN) density developed by Y. Ma and M.G. Genton in 2004. The main novelty is the existence of a fifth-order degree term in the polynomial that appears in the cumulative distribution function of such a density. In this case, we prove that our density has at most three modes under certain conditions for the parameters. Leveraging this new approach eases the modeling of data consisting of three subpopulations. For validation, we present examples of both univariate and multivariate cases using demographic data from the Human Mortality Data Base (HMD).

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  • Bufalo, Michele & NIGRI, ANDREA, 2024. "Trimodal extension based on the flexible generalized skew-normal distribution," OSF Preprints axu6g, Center for Open Science.
    • Handle: RePEc:osf:osfxxx:axu6g
    DOI: 10.31219/osf.io/axu6g
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    1. Yanyuan Ma & Marc G. Genton, 2004. "Flexible Class of Skew‐Symmetric Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(3), pages 459-468, September.
    2. Reinaldo B. Arellano‐Valle & Adelchi Azzalini, 2006. "On the Unification of Families of Skew‐normal Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 561-574, September.
    3. Adelchi Azzalini, 2005. "The Skew‐normal Distribution and Related Multivariate Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(2), pages 159-188, June.
    4. 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.
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