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Different Estimation Methods for Type I Half-Logistic Topp–Leone Distribution

Author

Listed:
  • Ramadan A. ZeinEldin

    (Deanship of Scientific Research, King AbdulAziz University, Jeddah 21442, Saudi Arabia
    Faculty of Graduate Studies for Statistical Research, Cairo University, Cairo 11865, Egypt)

  • Christophe Chesneau

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

  • Farrukh Jamal

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

  • Mohammed Elgarhy

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

Abstract

In this study, we propose a new flexible two-parameter continuous distribution with support on the unit interval. It can be identified as a special member of the so-called type I half-logistic-G family of distributions, defined with the Topp–Leone distribution as baseline. Among its features, the corresponding probability density function can be left skewed, right-skewed, approximately symmetric, J-shaped, as well as reverse J-shaped, making it suitable for modeling a wide variety of data sets. It thus provides an alternative to the so-called beta and Kumaraswamy distributions. The mathematical properties of the new distribution are determined, deriving the asymptotes, shapes, quantile function, skewness, kurtosis, some power series expansions, ordinary moments, incomplete moments, moment-generating function, stress strength parameter, and order statistics. Then, a statistical treatment of the related model is proposed. The estimation of the unknown parameters is performed by a simulation study exploring seven methods, all described in detail. Two practical data sets are analyzed, showing the usefulness of the new proposed model.

Suggested Citation

  • Ramadan A. ZeinEldin & Christophe Chesneau & Farrukh Jamal & Mohammed Elgarhy, 2019. "Different Estimation Methods for Type I Half-Logistic Topp–Leone Distribution," Mathematics, MDPI, vol. 7(10), pages 1-23, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:985-:d:277506
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    References listed on IDEAS

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    1. M. E. Ghitany & S. Kotz & M. Xie, 2005. "On some reliability measures and their stochastic orderings for the Topp-Leone distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(7), pages 715-722.
    2. Saralees Nadarajah & Samuel Kotz, 2003. "Moments of some J-shaped distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(3), pages 311-317.
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