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On the robustness of an epsilon skew extension for Burr III distribution on the real line

Author

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  • Mehmet Niyazi Çankaya

    (Applied Sciences School, Department of International Trading
    Uşak University)

  • Abdullah Yalçınkaya

    (Ankara University)

  • Ömer Altındaǧ

    (Bilecik Şeyh Edebali University)

  • Olcay Arslan

    (Ankara University)

Abstract

Burr III (BIII) distribution is used in a wide variety of fields, such as lifetime data analysis, reliability theory, and financial literature, and suchlike. It is defined on the positive axis and has two shape parameters, say c and k. These shape parameters make the distribution quite flexible. They also control the tail behaviour of the distribution. In this study, we extend BIII distribution to the real line and also add a skewness parameter, say $$\varepsilon $$ ε , with an epsilon skew extension approach. When the parameters c and k have a relationship such that $$ck \le 1 $$ c k ≤ 1 , it is skew unimodal. Otherwise, it is skew bimodal with the same level of peaks on the negative and positive sides of the real line. Thus, the epsilon skew extension of Burr III (ESBIII) distribution with only three parameters can provide adequate fits for data sets that may have heavy-tailedness, skewness, unimodality or bimodality. A location-scale form of this distribution is also given. Distributional properties are investigated. The maximum likelihood (ML) estimation method for the parameters of ESBIII is considered. The robustness properties of the ML estimators are studied in terms of the boundedness of the influence function. Further, tail behaviour of ESBIII distribution is also examined to explore the robustness of ESBIII distribution against the outliers. The modelling capacity of this distribution is illustrated using two real data examples.

Suggested Citation

  • Mehmet Niyazi Çankaya & Abdullah Yalçınkaya & Ömer Altındaǧ & Olcay Arslan, 2019. "On the robustness of an epsilon skew extension for Burr III distribution on the real line," Computational Statistics, Springer, vol. 34(3), pages 1247-1273, September.
    • Handle: RePEc:spr:compst:v:34:y:2019:i:3:d:10.1007_s00180-018-0859-y
    DOI: 10.1007/s00180-018-0859-y
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    References listed on IDEAS

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    1. Mineo, Angelo & Ruggieri, Mariantonietta, 2005. "A Software Tool for the Exponential Power Distribution: The normalp Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 12(i04).
    2. M. C. Jones & M. J. Faddy, 2003. "A skew extension of the t‐distribution, with applications," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 159-174, February.
    3. A. Jamalizadeh & A. Arabpour & N. Balakrishnan, 2011. "A generalized skew two-piece skew-normal distribution," Statistical Papers, Springer, vol. 52(2), pages 431-446, May.
    4. Sukru Acitas & Pelin Kasap & Birdal Senoglu & Olcay Arslan, 2013. "One-step M -estimators: Jones and Faddy's skewed t -distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(7), pages 1545-1560, July.
    5. Ali Genç, 2013. "A skew extension of the slash distribution via beta-normal distribution," Statistical Papers, Springer, vol. 54(2), pages 427-442, May.
    6. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    7. Shao, Quanxi & Chen, Yongqin D. & Zhang, Lu, 2008. "An extension of three-parameter Burr III distribution for low-flow frequency analysis," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1304-1314, January.
    8. Wenhao Gui, 2014. "A generalization of the slashed distribution via alpha skew normal distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(4), pages 547-563, November.
    9. M.Y. Hassan & M.Y. El-Bassiouni, 2016. "Bimodal skew-symmetric normal distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(5), pages 1527-1541, March.
    10. Purdom Elizabeth & Holmes Susan P, 2005. "Error Distribution for Gene Expression Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-35, July.
    11. Jizba, Petr & Korbel, Jan, 2016. "On q-non-extensive statistics with non-Tsallisian entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 808-827.
    12. Çankaya, Mehmet Niyazi & Korbel, Jan, 2017. "On statistical properties of Jizba–Arimitsu hybrid entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 475(C), pages 1-10.
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