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Statistical Properties and Different Methods of Estimation for Type I Half Logistic Inverted Kumaraswamy Distribution

Author

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  • Ramadan A. ZeinEldin

    (Deanship of Scientific Research, King AbdulAziz University, Jeddah 21589, Saudi Arabia
    Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt)

  • Christophe Chesneau

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

  • Farrukh Jamal

    (Department of Statistics, Govt. S.A Postgraduate College Dera Nawab Sahib, Bahawalpur, Punjab 63360, Pakistan)

  • Mohammed Elgarhy

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

Abstract

In this paper, we introduce and study a new three-parameter lifetime distribution constructed from the so-called type I half-logistic-G family and the inverted Kumaraswamy distribution, naturally called the type I half-logistic inverted Kumaraswamy distribution. The main feature of this new distribution is to add a new tuning parameter to the inverted Kumaraswamy (according to the type I half-logistic structure), with the aim to increase the flexibility of the related inverted Kumaraswamy model and thus offering more precise diagnostics in data analyses. The new distribution is discussed in detail, exhibiting various mathematical and statistical properties, with related graphics and numerical results. An exhaustive simulation was conducted to investigate the estimation of the model parameters via several well-established methods, including the method of maximum likelihood estimation, methods of least squares and weighted least squares estimation, and method of Cramer-von Mises minimum distance estimation, showing their numerical efficiency. Finally, by considering the method of maximum likelihood estimation, we apply the new model to fit two practical data sets. In this regards, it is proved to be better than recent models, also derived to the inverted Kumaraswamy distribution.

Suggested Citation

  • Ramadan A. ZeinEldin & Christophe Chesneau & Farrukh Jamal & Mohammed Elgarhy, 2019. "Statistical Properties and Different Methods of Estimation for Type I Half Logistic Inverted Kumaraswamy Distribution," Mathematics, MDPI, vol. 7(10), pages 1-24, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:1002-:d:279116
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    References listed on IDEAS

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    1. Masood Anwar & Amna Bibi, 2018. "The Half-Logistic Generalized Weibull Distribution," Journal of Probability and Statistics, Hindawi, vol. 2018, pages 1-12, January.
    2. David Hinkley, 1977. "On Quick Choice of Power Transformation," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(1), pages 67-69, March.
    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. Masood Anwar & Jawaria Zahoor, 2018. "The Half-Logistic Lomax Distribution for Lifetime Modeling," Journal of Probability and Statistics, Hindawi, vol. 2018, pages 1-12, February.
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