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Type II Topp Leone Power Lomax Distribution with Applications

Author

Listed:
  • Sanaa Al-Marzouki

    (Statistics Department, Faculty of Science, King AbdulAziz University, Jeddah 21551, Saudi Arabia)

  • 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

In many areas of applied sciences, the last step of a study often consists in analyzing in depth the collected data. Among all the kinds of data, the lifetime data are well-known to convey a great deal of information whose capture is necessary to identify one or more key phenomena. In this regards, numerous mathematical models have been proposed, including those based on lifetime distributions. In this paper, we introduce a new four-parameter lifetime distribution based on the type II Topp-Leone-G family and the power Lomax distribution. In comparison to the existing distributions, the new one is characterized by very flexible probability functions: increasing, decreasing, J, and reverse J shapes are observed for the probability density and hazard rate functions, giving first signs on the potential of adaptability of the related model. With this idea in mind, the new distribution is studied in detail, from both the theoretical and applied sides. After showing its main mathematical properties, the related model is investigated with estimation of the parameters by the maximum likelihood method. We applied it to two practical datasets, including the well-know aircraft windshield data. We show that the new model performs better than several modern adversary models, motivating its use in an applied setting.

Suggested Citation

  • Sanaa Al-Marzouki & Farrukh Jamal & Christophe Chesneau & Mohammed Elgarhy, 2019. "Type II Topp Leone Power Lomax Distribution with Applications," Mathematics, MDPI, vol. 8(1), pages 1-26, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2019:i:1:p:4-:d:299443
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    References listed on IDEAS

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    3. M. E. Mead, 2015. "Generalized Inverse Gamma Distribution and its Application in Reliability," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(7), pages 1426-1435, April.
    4. Carl M. Harris, 1968. "The Pareto Distribution as a Queue Service Discipline," Operations Research, INFORMS, vol. 16(2), pages 307-313, April.
    5. 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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