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On Burr III Marshal Olkin family: development, properties, characterizations and applications

Author

Listed:
  • Fiaz Ahmad Bhatti

    (National College of Business Administration and Economics)

  • G. G. Hamedani

    (Marquette University)

  • Mustafa C. Korkmaz

    (Artvin Çoruh University)

  • Gauss M. Cordeiro

    (UniversidadeFederaldePernambuco)

  • Haitham M. Yousof

    (Benha University)

  • Munir Ahmad

    (National College of Business Administration and Economics)

Abstract

In this paper, a flexible family of distributions with unimodel, bimodal, increasing, increasing and decreasing, inverted bathtub and modified bathtub hazard rate called Burr III-Marshal Olkin-G (BIIIMO-G) family is developed on the basis of the T-X family technique. The density function of the BIIIMO-G family is arc, exponential, left- skewed, right-skewed and symmetrical shaped. Descriptive measures such as quantiles, moments, incomplete moments, inequality measures and reliability measures are theoretically established. The BIIIMO-G family is characterized via different techniques. Parameters of the BIIIMO-G family are estimated using maximum likelihood method. A simulation study is performed to illustrate the performance of the maximum likelihood estimates (MLEs). The potentiality of BIIIMO-G family is demonstrated by its application to real data sets.

Suggested Citation

  • Fiaz Ahmad Bhatti & G. G. Hamedani & Mustafa C. Korkmaz & Gauss M. Cordeiro & Haitham M. Yousof & Munir Ahmad, 2019. "On Burr III Marshal Olkin family: development, properties, characterizations and applications," Journal of Statistical Distributions and Applications, Springer, vol. 6(1), pages 1-21, December.
    • Handle: RePEc:spr:jstada:v:6:y:2019:i:1:d:10.1186_s40488-019-0101-7
    DOI: 10.1186/s40488-019-0101-7
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    References listed on IDEAS

    as
    1. Haitham M. Yousof & Ahmed Z. Afify & Saralees Nadarajah & Gokarna R. Aryal, 2018. "The Marshall-Olkin Generalized-G Family Of Distributions With Applications," Statistica, Department of Statistics, University of Bologna, vol. 78(3), pages 273-295.
    2. Gauss Cordeiro & Artur Lemonte, 2013. "On the Marshall–Olkin extended Weibull distribution," Statistical Papers, Springer, vol. 54(2), pages 333-353, May.
    3. 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.
    4. M. H. Tahir & Gauss M. Cordeiro & Ayman Alzaatreh & M. Mansoor & M. Zubair, 2016. "The logistic-X family of distributions and its applications," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(24), pages 7326-7349, December.
    5. Miroslav Ristić & Debasis Kundu, 2015. "Marshall-Olkin generalized exponential distribution," METRON, Springer;Sapienza Università di Roma, vol. 73(3), pages 317-333, December.
    6. K. Jose & Shanoja Naik & Miroslav Ristić, 2010. "Marshall–Olkin q-Weibull distribution and max–min processes," Statistical Papers, Springer, vol. 51(4), pages 837-851, December.
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