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Mastering the Body and Tail Shape of a Distribution

Author

Listed:
  • Matthias Wagener

    (Department of Statistics, University of Pretoria, Pretoria 0002, South Africa)

  • Andriette Bekker

    (Department of Statistics, University of Pretoria, Pretoria 0002, South Africa)

  • Mohammad Arashi

    (Department of Statistics, University of Pretoria, Pretoria 0002, South Africa
    Department of Statistics, Ferdowsi University of Mashhad, Mashhad 4897, Iran)

Abstract

The normal distribution and its perturbation have left an immense mark on the statistical literature. Several generalized forms exist to model different skewness, kurtosis, and body shapes. Although they provide better fitting capabilities, these generalizations do not have parameters and formulae with a clear meaning to the practitioner on how the distribution is being modeled. We propose a neat integration approach generalization which intuitively gives direct control of the body and tail shape, the body-tail generalized normal (BTGN). The BTGN provides the basis for a flexible distribution, emphasizing parameter interpretation, estimation properties, and tractability. Basic statistical measures are derived, such as the density function, cumulative density function, moments, moment generating function. Regarding estimation, the equations for maximum likelihood estimation and maximum product spacing estimation are provided. Finally, real-life situations data, such as log-returns, time series, and finite mixture modeling, are modeled using the BTGN. Our results show that it is possible to have more desirable traits in a flexible distribution while still providing a superior fit to industry-standard distributions, such as the generalized hyperbolic, generalized normal, tail-inflated normal, and t distributions.

Suggested Citation

  • Matthias Wagener & Andriette Bekker & Mohammad Arashi, 2021. "Mastering the Body and Tail Shape of a Distribution," Mathematics, MDPI, vol. 9(21), pages 1-22, October.
  • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2648-:d:660453
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    References listed on IDEAS

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