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A New Three-Parameter Exponential Distribution with Variable Shapes for the Hazard Rate: Estimation and Applications

Author

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  • Ahmed Z. Afify

    (Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt)

  • Osama Abdo Mohamed

    (Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44511, Egypt)

Abstract

In this paper, we study a new flexible three-parameter exponential distribution called the extended odd Weibull exponential distribution, which can have constant, decreasing, increasing, bathtub, upside-down bathtub and reversed-J shaped hazard rates, and right-skewed, left-skewed, symmetrical, and reversed-J shaped densities. Some mathematical properties of the proposed distribution are derived. The model parameters are estimated via eight frequentist estimation methods called, the maximum likelihood estimators, least squares and weighted least-squares estimators, maximum product of spacing estimators, Cramér-von Mises estimators, percentiles estimators, and Anderson-Darling and right-tail Anderson-Darling estimators. Extensive simulations are conducted to compare the performance of these estimation methods for small and large samples. Four practical data sets from the fields of medicine, engineering, and reliability are analyzed, proving the usefulness and flexibility of the proposed distribution.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:135-:d:309748
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    References listed on IDEAS

    as
    1. Abbas Mahdavi & Debasis Kundu, 2017. "A new method for generating distributions with an application to exponential distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(13), pages 6543-6557, July.
    2. 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.
    3. Luis Gustavo Bastos Pinho & Gauss Moutinho Cordeiro & Juvêncio Santos Nobre, 2015. "The Harris Extended Exponential Distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(16), pages 3486-3502, August.
    4. Nadarajah, Saralees & Kotz, Samuel, 2006. "The beta exponential distribution," Reliability Engineering and System Safety, Elsevier, vol. 91(6), pages 689-697.
    Full references (including those not matched with items on IDEAS)

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