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The Transmuted Odd Fréchet-G Family of Distributions: Theory and Applications

Author

Listed:
  • Majdah M. Badr

    (Statistics Department, Faculty of Science for Girls, University of Jeddah, P. O. Box 70973, Jeddah 21577, Saudi Arabia)

  • Ibrahim Elbatal

    (Department of Mathematics and Statistics, College of Science Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
    Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt)

  • Farrukh Jamal

    (Department of Statistics, Govt. S.A Postgraduate College Dera Nawab Sahib, Bahawalpur, Punjab 63100, Pakistan)

  • Christophe Chesneau

    (Department of Mathematics, Université de Caen, LMNO, Campus II, Science 3, 14032 Caen, France)

  • Mohammed Elgarhy

    (Valley High Institute for Management Finance and Information Systems, Obour, Qaliubia 11828, Egypt)

Abstract

The last years, the odd Fréchet-G family has been considered with success in various statistical applications. This notoriety can be explained by its simple and flexible exponential-odd structure quite different to the other existing families, with the use of only one additional parameter. In counter part, some of its statistical properties suffer of a lack of adaptivity in the sense that they really depend on the choice of the baseline distribution. Hence, efforts have been made to relax this subjectivity by investigating extensions or generalizations of the odd transformation at the heart of the construction of this family, with the aim to reach new perspectives of applications as well. This study explores another possibility, based on the transformation of the whole cumulative distribution function of this family (while keeping the odd transformation intact), through the use of the quadratic rank transmutation that has proven itself in other contexts. We thus introduce and study a new family of flexible distributions called the transmuted odd Fréchet-G family. We show how the former odd Fréchet-G family is enriched by the proposed transformation through theoretical and practical results. We emphasize the special distribution based on the standard exponential distribution because of its desirable features for the statistical modeling. In particular, different kinds of monotonic and nonmonotonic shapes for the probability density and hazard rate functions are observed. Then, we show how the new family can be used in practice. We discuss in detail the parametric estimation of a special model, along with a simulation study. Practical data sets are handle with quite favorable results for the new modeling strategy.

Suggested Citation

  • Majdah M. Badr & Ibrahim Elbatal & Farrukh Jamal & Christophe Chesneau & Mohammed Elgarhy, 2020. "The Transmuted Odd Fréchet-G Family of Distributions: Theory and Applications," Mathematics, MDPI, vol. 8(6), pages 1-20, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:958-:d:370059
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    References listed on IDEAS

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    1. Ayman Alzaatreh & Carl Lee & Felix Famoye, 2013. "A new method for generating families of continuous distributions," METRON, Springer;Sapienza Università di Roma, vol. 71(1), pages 63-79, June.
    2. Zohdy M. Nofal & Ahmed Z. Afify & Haitham M. Yousof & Gauss M. Cordeiro, 2017. "The generalized transmuted-G family of distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(8), pages 4119-4136, April.
    3. Girish Babu Moolath & Jayakumar K, 2017. "T-Transmuted X Family of Distributions," Statistica, Department of Statistics, University of Bologna, vol. 77(3), pages 251-276.
    4. William T. Shaw & Ian R. C. Buckley, 2009. "The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map," Papers 0901.0434, arXiv.org.
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