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On the Analysis of New COVID-19 Cases in Pakistan Using an Exponentiated Version of the M Family of Distributions

Author

Listed:
  • Rashad A. R. Bantan

    (Department of Marine Geology, Faculty of Marine Science, King Abdulaziz University, Jeddah 21551, Saudi Arabia)

  • 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 63100, Punjab, Pakistan)

  • Mohammed Elgarhy

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

Abstract

This paper develops the exponentiated Mfamily of continuous distributions, aiming to provide new statistical models for data fitting purposes. It stands out from the other families, as it depends on two baseline distributions, with the use of ratio and power transforms in the definition of the main cumulative distribution function. Thanks to the joint action of the possibly different baseline distributions, flexible statistical models can be created, motivating a complete study in this regard. Thus, we discuss the theoretical properties of the new family, with emphasis on those of potential interest to the overall probability and statistics. Then, a new three-parameter lifetime distribution is derived, with the choices of the inverse exponential and exponential distributions as baselines. After pointing out the great flexibility of the related model, we apply it to analyze an actual dataset of current interest: the daily COVID-19 cases observed in Pakistan from 21 March to 29 May 2020 (inclusive). As notable results, we demonstrate that the proposed model is the best among the 15 top ranked models in the literature, including the inverse exponential and exponential models, several modern extensions of them depending on more parameters, and the “unexponentiated” version of the proposed model as well. As future perspectives, the proposed model can be of interest to analyze data on COVID-19 cases in other countries, for possible comparison studies.

Suggested Citation

  • Rashad A. R. Bantan & Christophe Chesneau & Farrukh Jamal & Mohammed Elgarhy, 2020. "On the Analysis of New COVID-19 Cases in Pakistan Using an Exponentiated Version of the M Family of Distributions," Mathematics, MDPI, vol. 8(6), pages 1-20, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:953-:d:369987
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    References listed on IDEAS

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    2. Maha A Aldahlan & Farrukh Jamal & Christophe Chesneau & Ibrahim Elbatal & Mohammed Elgarhy, 2020. "Exponentiated power generalized Weibull power series family of distributions: Properties, estimation and applications," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-25, March.
    3. Saralees Nadarajah, 2011. "The exponentiated exponential distribution: a survey," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(3), pages 219-251, September.
    4. M. Jones, 2004. "Families of distributions arising from distributions of order statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 1-43, June.
    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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    Cited by:

    1. 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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