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

  • Mehmet Niyazi Çankaya
  • Abdullah Yalçınkaya
  • Ömer Altındaǧ
  • Olcay Arslan
Original Paper
  • 71 Downloads

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 \(\varepsilon \), with an epsilon skew extension approach. When the parameters c and k have a relationship such that \(ck \le 1 \), 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.

Keywords

Burr III distribution Epsilon skew extension Asymmetry Robustness Bimodality Unimodality 

Notes

Acknowledgements

We thank the anonymous reviewers for their careful reading of our manuscript and their many insightful comments and suggestions. We would like to say our special thanks to the Editorial Board Members. We thank the native speaker who supported us for representation in the formal organization of this paper.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Mehmet Niyazi Çankaya
    • 1
    • 2
  • Abdullah Yalçınkaya
    • 3
  • Ömer Altındaǧ
    • 4
  • Olcay Arslan
    • 3
  1. 1.Applied Sciences School, Department of International TradingUşakTurkey
  2. 2.Department of Statistics, Faculty of Arts and SciencesUşak UniversityUşakTurkey
  3. 3.Department of Statistics, Faculty of ScienceAnkara UniversityAnkaraTurkey
  4. 4.Department of Statistics, Faculty of Arts and SciencesBilecik Şeyh Edebali UniversityBilecikTurkey

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