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Inferences from Asymmetric Multivariate Exponential Power Distribution

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  • A. T. Soyinka

    (Federal University of Agriculture Alabata)

  • A. A. Olosunde

    (Obafemi Awolowo University)

Abstract

In this paper, we develop the asymptotic distribution of the covariance structure of an asymmetric multivariate exponential power distribution (AMEPD) by extending the existing Hotelling t2 distribution to its generalized form. The obtained results ‘generalised Hotelling t2 test statistic’, accommodates for the existing Mahalanobis distance between two multivariate data sets. The hazard rate and the characteristics function of the desired test statistics are established. The study further establishes the test of hypothesis and simultaneous confidence interval for the population mean vectors of p th attributes from AMEPD by using the Neymar-Pearson lemma and Pivotal quantity approaches. The obtained results, which are dependent on shape parameter flexibility and skewness parameter, generalize the test of hypothesis and simultaneous confidence intervals of various distributions which are members of the exponential power family. Simulated and real life data were used to demonstrate the usefulness of the obtained results.

Suggested Citation

  • A. T. Soyinka & A. A. Olosunde, 2021. "Inferences from Asymmetric Multivariate Exponential Power Distribution," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 350-370, November.
    • Handle: RePEc:spr:sankhb:v:83:y:2021:i:2:d:10.1007_s13571-020-00235-w
    DOI: 10.1007/s13571-020-00235-w
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    References listed on IDEAS

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    1. Ivana Komunjer, 2007. "Asymmetric power distribution: Theory and applications to risk measurement," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(5), pages 891-921.
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    3. Zhu, Dongming & Zinde-Walsh, Victoria, 2009. "Properties and estimation of asymmetric exponential power distribution," Journal of Econometrics, Elsevier, vol. 148(1), pages 86-99, January.
    4. Saralees Nadarajah & Mahdi Teimouri, 2012. "On the Characteristic Function for Asymmetric Exponential Power Distributions," Econometric Reviews, Taylor & Francis Journals, vol. 31(4), pages 475-481.
    5. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
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