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Generalized inverted Kumaraswamy generated family of distributions: theory and applications

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  • Farrukh Jamal
  • Muhammad Arslan Nasir
  • Gamze Ozel
  • M. Elgarhy
  • Naushad Mamode Khan

Abstract

This paper proposes a new generator function based on the inverted Kumaraswamy distribution and introduces ‘generalized inverted Kumaraswamy-G’ family of distributions. We provide a comprehensive account of some of its mathematical properties that include the ordinary and incomplete moments, quantile and generating functions and order statistics. The infinite mixture representations for probability density and cumulative distribution and entropy functions of the new family are also established. The density function of the ith-order statistics is expressed as an infinite linear combination of baseline densities and model parameters are estimated by maximum likelihood method. Four special models of this family are also derived along with their respective hazard rate functions. The maximum likelihood estimation (MLE) method is used to obtain the model parameters. Monte Carlo simulation experiments are executed to assess the performance of the ML estimators under the corresponding generated models while some data applications are also illustrated. The results of the study show that the proposed distribution is more flexible as compared to the baseline model. This distribution especially can be used to model symmetric, left-skewed, right-skewed and reversed-J data sets.

Suggested Citation

  • Farrukh Jamal & Muhammad Arslan Nasir & Gamze Ozel & M. Elgarhy & Naushad Mamode Khan, 2019. "Generalized inverted Kumaraswamy generated family of distributions: theory and applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(16), pages 2927-2944, December.
    • Handle: RePEc:taf:japsta:v:46:y:2019:i:16:p:2927-2944
    DOI: 10.1080/02664763.2019.1623867
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    Cited by:

    1. Joseph Thomas Eghwerido & Pelumi E. Oguntunde & Friday Ikechukwu Agu, 2023. "The Alpha Power Marshall-Olkin-G Distribution: Properties, and Applications," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 172-197, February.
    2. Rana Muhammad Imran Arshad & Muhammad Hussain Tahir & Christophe Chesneau & Farrukh Jamal, 2020. "The Gamma Kumaraswamy-G family of distributions: theory, inference and applications," Statistics in Transition New Series, Polish Statistical Association, vol. 21(5), pages 17-40, December.
    3. Salem A. Alyami & Ibrahim Elbatal & Naif Alotaibi & Ehab M. Almetwally & Mohammed Elgarhy, 2022. "Modeling to Factor Productivity of the United Kingdom Food Chain: Using a New Lifetime-Generated Family of Distributions," Sustainability, MDPI, vol. 14(14), pages 1-28, July.

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