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The Marshall-Olkin logistic-exponential distribution

Author

Listed:
  • M. Mansoor
  • M. H. Tahir
  • Gauss M. Cordeiro
  • Serge B. Provost
  • Ayman Alzaatreh

Abstract

We introduce a three-parameter extension of the exponential distribution which contains as sub-models the exponential, logistic-exponential and Marshall-Olkin exponential distributions. The new model is very flexible and its associated density function can be decreasing or unimodal. Further, it can produce all of the four major shapes of the hazard rate, that is, increasing, decreasing, bathtub and upside-down bathtub. Given that closed-form expressions are available for the survival and hazard rate functions, the new distribution is quite tractable. It can be used to analyze various types of observations including censored data. Computable representations of the quantile function, ordinary and incomplete moments, generating function and probability density function of order statistics are obtained. The maximum likelihood method is utilized to estimate the model parameters. A simulation study is carried out to assess the performance of the maximum likelihood estimators. Two actual data sets are used to illustrate the applicability of the proposed model.

Suggested Citation

  • M. Mansoor & M. H. Tahir & Gauss M. Cordeiro & Serge B. Provost & Ayman Alzaatreh, 2019. "The Marshall-Olkin logistic-exponential distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(2), pages 220-234, January.
    • Handle: RePEc:taf:lstaxx:v:48:y:2019:i:2:p:220-234
    DOI: 10.1080/03610926.2017.1414254
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    Cited by:

    1. Ahmed Z. Afify & Osama Abdo Mohamed, 2020. "A New Three-Parameter Exponential Distribution with Variable Shapes for the Hazard Rate: Estimation and Applications," Mathematics, MDPI, vol. 8(1), pages 1-17, January.
    2. Mashail M. AL Sobhi, 2020. "The Inverse-Power Logistic-Exponential Distribution: Properties, Estimation Methods, and Application to Insurance Data," Mathematics, MDPI, vol. 8(11), pages 1-15, November.
    3. Odom Conleth Chinazom & Nduka Ethelbert Chinaka & Ijomah Maxwell Azubuike, 2019. "The Marshall-Olkin Extended Weibull-Exponential Distribution: Properties and Applications," Journal of Asian Scientific Research, Asian Economic and Social Society, vol. 9(10), pages 158-172, October.
    4. Isidro Jesús González-Hernández & Rafael Granillo-Macías & Carlos Rondero-Guerrero & Isaías Simón-Marmolejo, 2021. "Marshall-Olkin distributions: a bibliometric study," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(11), pages 9005-9029, November.

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