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A new generalized family of distributions based on combining Marshal-Olkin transformation with T-X family

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  • Hadeel Klakattawi
  • Dawlah Alsulami
  • Mervat Abd Elaal
  • Sanku Dey
  • Lamya Baharith

Abstract

Data analysis in real life often relies mainly on statistical probability distributions. However, data arising from different fields such as environmental, financial, biomedical sciences and other areas may not fit the classical distributions. Therefore, the need arises for developing new distributions that would capture high degree of skewness and kurtosis and enhance the goodness-of-fit in empirical distribution. In this paper, we introduce a novel family of distributions which can extend some popular classes of distributions to include different new versions of the baseline distributions. The proposed family of distributions is referred as the Marshall-Olkin Weibull generated family. The proposed family of distributions is a combination of Marshall-Olkin transformation and the Weibull generated family. Two special members of the proposed family are investigated. A variety of shapes for the densities and hazard rate are presented of the considered sub-models. Some of the main mathematical properties of this family are derived. The estimation for the parameters is obtained via the maximum likelihood method. Moreover, the performance of the estimators for the considered members is examined through simulation studies in terms of bias and root mean square error. Besides, based on the new generated family, the log Marshall-Olkin Weibull-Weibull regression model for censored data is proposed. Finally, COVID-19 data and three lifetime data sets are used to demonstrate the importance of the newly proposed family. Through such an applications, it is shown that this family of distributions provides a better fit when compared with other competitive distributions.

Suggested Citation

  • Hadeel Klakattawi & Dawlah Alsulami & Mervat Abd Elaal & Sanku Dey & Lamya Baharith, 2022. "A new generalized family of distributions based on combining Marshal-Olkin transformation with T-X family," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-29, February.
    • Handle: RePEc:plo:pone00:0263673
    DOI: 10.1371/journal.pone.0263673
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    References listed on IDEAS

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    1. Muhammad Ahsan Ul Haq & G. G. Hamedani & M. Elgarhy & Pedro Luiz Ramos, 2020. "Marshall-Olkin Power Lomax Distribution: Properties and Estimation Based on Complete and Censored Samples," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 9(1), pages 1-48, January.
    2. Gauss Cordeiro & Artur Lemonte, 2013. "On the Marshall–Olkin extended Weibull distribution," Statistical Papers, Springer, vol. 54(2), pages 333-353, May.
    3. Richard L. Smith & J. C. Naylor, 1987. "A Comparison of Maximum Likelihood and Bayesian Estimators for the Three‐Parameter Weibull Distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 358-369, November.
    4. M. E. Ghitany & E. K. Al-Hussaini & R. A. Al-Jarallah, 2005. "Marshall-Olkin extended weibull distribution and its application to censored data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(10), pages 1025-1034.
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    1. Harsh Tripathi & Varun Agiwal, 2024. "A new version of univariate Rayleigh distribution: properties, estimation and it’s application," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 15(11), pages 5367-5377, November.

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