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On application of the univariate Kotz distribution and some of its extensions

Author

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  • Mahdi Salehi

    (University of Neyshabur)

  • Adelchi Azzalini

    (University of Padua)

Abstract

Despite a flourishing activity, especially in recent times, for the study of flexible parametric classes of distributions, little work has dealt with the case where the tail weight and degree of peakedness is regulated by two parameters instead of a single one, as it is usually the case. The present contribution starts off from the symmetric distributions introduced by Kotz in 1975, subsequently evolved into the so-called Kotz-type distribution, and builds on their univariate versions by introducing a parameter which allows for the presence of asymmetry. We study some formal properties of these distributions and examine their practical usefulness in some real-data illustrations, considering both symmetric and asymmetric variants of the distributions.

Suggested Citation

  • Mahdi Salehi & Adelchi Azzalini, 2018. "On application of the univariate Kotz distribution and some of its extensions," METRON, Springer;Sapienza Università di Roma, vol. 76(2), pages 177-201, August.
    • Handle: RePEc:spr:metron:v:76:y:2018:i:2:d:10.1007_s40300-018-0137-3
    DOI: 10.1007/s40300-018-0137-3
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    References listed on IDEAS

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    1. Umbach, Dale, 2006. "Some moment relationships for skew-symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 76(5), pages 507-512, March.
    2. repec:eca:wpaper:2013/128686 is not listed on IDEAS
    3. M. C. Jones, 2015. "On Families of Distributions with Shape Parameters," International Statistical Review, International Statistical Institute, vol. 83(2), pages 175-192, August.
    4. Cedric Flecher & Denis Allard & Philippe Naveau, 2010. "Truncated skew-normal distributions: moments, estimation by weighted moments and application to climatic data," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 331-345.
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    Cited by:

    1. Mahdi Salehi & Andriette Bekker & Mohammad Arashi, 2023. "A Semi-parametric Density Estimation with Application in Clustering," Journal of Classification, Springer;The Classification Society, vol. 40(1), pages 52-78, April.

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