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Kumaraswamy Generalized Power Lomax Distributionand Its Applications

Author

Listed:
  • Vasili B.V. Nagarjuna

    (Department of Statistics, Pondicherry University, Pondicherry 605 014, India)

  • R. Vishnu Vardhan

    (Department of Statistics, Pondicherry University, Pondicherry 605 014, India)

  • Christophe Chesneau

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

Abstract

In this paper, a new five-parameter distribution is proposed using the functionalities of the Kumaraswamy generalized family of distributions and the features of the power Lomax distribution. It is named as Kumaraswamy generalized power Lomax distribution. In a first approach, we derive its main probability and reliability functions, with a visualization of its modeling behavior by considering different parameter combinations. As prime quality, the corresponding hazard rate function is very flexible; it possesses decreasing, increasing and inverted (upside-down) bathtub shapes. Also, decreasing-increasing-decreasing shapes are nicely observed. Some important characteristics of the Kumaraswamy generalized power Lomax distribution are derived, including moments, entropy measures and order statistics. The second approach is statistical. The maximum likelihood estimates of the parameters are described and a brief simulation study shows their effectiveness. Two real data sets are taken to show how the proposed distribution can be applied concretely; parameter estimates are obtained and fitting comparisons are performed with other well-established Lomax based distributions. The Kumaraswamy generalized power Lomax distribution turns out to be best by capturing fine details in the structure of the data considered.

Suggested Citation

  • Vasili B.V. Nagarjuna & R. Vishnu Vardhan & Christophe Chesneau, 2021. "Kumaraswamy Generalized Power Lomax Distributionand Its Applications," Stats, MDPI, vol. 4(1), pages 1-18, January.
    • Handle: RePEc:gam:jstats:v:4:y:2021:i:1:p:3-45:d:476207
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    References listed on IDEAS

    as
    1. Amal S. Hassan & Marwa Abd-Allah, 2019. "On the Inverse Power Lomax Distribution," Annals of Data Science, Springer, vol. 6(2), pages 259-278, June.
    2. Gauss Cordeiro & Saralees Nadarajah & Edwin Ortega, 2012. "The Kumaraswamy Gumbel distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(2), pages 139-168, June.
    3. 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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    Cited by:

    1. Lucas D. Ribeiro Reis & Gauss M. Cordeiro & Maria do Carmo S. Lima, 2022. "The Stacy-G Class: A New Family of Distributions with Regression Modeling and Applications to Survival Real Data," Stats, MDPI, vol. 5(1), pages 1-43, March.

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