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The polar-generalized normal distribution: properties, Bayesian estimation and applications

Author

Listed:
  • Masoud Faridi

    (Tarbiat Modares University)

  • Majid Jafari Khaledi

    (Tarbiat Modares University)

Abstract

This paper introduces an extension to the normal distribution through the polar method to capture bimodality and asymmetry, which are often observed characteristics of empirical data. The later two features are entirely controlled by a separate scalar parameter. Explicit expressions for the cumulative distribution function, the density function and the moments were derived. The stochastic representation of the distribution facilitates implementing Bayesian estimation via the Markov chain Monte Carlo methods. Some real-life data as well as simulated data are analyzed to illustrate the flexibility of the distribution for modeling asymmetric bimodality.

Suggested Citation

  • Masoud Faridi & Majid Jafari Khaledi, 2022. "The polar-generalized normal distribution: properties, Bayesian estimation and applications," Statistical Papers, Springer, vol. 63(2), pages 571-603, April.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:2:d:10.1007_s00362-021-01245-0
    DOI: 10.1007/s00362-021-01245-0
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    References listed on IDEAS

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    1. Majid Khaledi & Firoozeh Rivaz, 2009. "Empirical Bayes spatial prediction using a Monte Carlo EM algorithm," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 18(1), pages 35-47, March.
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    6. Ali Genç, 2013. "A skew extension of the slash distribution via beta-normal distribution," Statistical Papers, Springer, vol. 54(2), pages 427-442, May.
    7. Zareifard, Hamid & Jafari Khaledi, Majid, 2013. "Non-Gaussian modeling of spatial data using scale mixing of a unified skew Gaussian process," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 16-28.
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