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The bivariate alpha-skew-normal distribution

Author

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  • Francisco Louzada
  • Anderson Ara
  • Guilherme Fernandes

Abstract

In this paper, we propose a new bivariate distribution, namely bivariate alpha-skew-normal distribution. The proposed distribution is very flexible and capable of generalizing the univariate alpha-skew-normal distribution as its marginal component distributions; it features a probability density function with up to two modes and has the bivariate normal distribution as a special case. The joint moment generating function as well as the main moments are provided. Inference is based on a usual maximum-likelihood estimation approach. The asymptotic properties of the maximum-likelihood estimates are verified in light of a simulation study. The usefulness of the new model is illustrated in a real benchmark data.

Suggested Citation

  • Francisco Louzada & Anderson Ara & Guilherme Fernandes, 2017. "The bivariate alpha-skew-normal distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(14), pages 7147-7156, July.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:14:p:7147-7156
    DOI: 10.1080/03610926.2015.1024865
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    Cited by:

    1. Jonas Baillien & Irène Gijbels & Anneleen Verhasselt, 2023. "Flexible asymmetric multivariate distributions based on two-piece univariate distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(1), pages 159-200, February.
    2. Na Young Yoo & Ji Hwan Cha, 2024. "General classes of bivariate distributions for modeling data with common observations," Statistical Papers, Springer, vol. 65(8), pages 5219-5238, October.

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