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Marshall-Olkin generalized exponential distribution

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  • Miroslav Ristić
  • Debasis Kundu

Abstract

Marshall and Olkin (Biometrika 641–652, 1997 ) introduced a new way of incorporating a parameter to expand a family of distributions. In this paper we adopt the Marshall-Olkin approach to introduce an extra shape parameter to the two-parameter generalized exponential distribution. It is observed that the new three-parameter distribution is very flexible. The probability density functions can be either a decreasing or an unimodal function. The hazard function of the proposed model, can have all the four major shapes, namely increasing, decreasing, bathtub or inverted bathtub types. Different properties of the proposed distribution have been established. The new family of distributions is analytically quite tractable, and it can be used quite effectively, to analyze censored data also. Maximum likelihood method is used to compute the estimators of the unknown parameters. Two data sets have been analyzed, and the results are quite satisfactory. Copyright Sapienza Università di Roma 2015

Suggested Citation

  • Miroslav Ristić & Debasis Kundu, 2015. "Marshall-Olkin generalized exponential distribution," METRON, Springer;Sapienza Università di Roma, vol. 73(3), pages 317-333, December.
    • Handle: RePEc:spr:metron:v:73:y:2015:i:3:p:317-333
    DOI: 10.1007/s40300-014-0056-x
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    References listed on IDEAS

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    1. Nandini Kannan & Debasis Kundu & P. Nair & R. C. Tripathi, 2010. "The generalized exponential cure rate model with covariates," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(10), pages 1625-1636.
    2. Bartoszewicz, Jaroslaw, 2001. "Stochastic comparisons of random minima and maxima from life distributions," Statistics & Probability Letters, Elsevier, vol. 55(1), pages 107-112, November.
    3. Kundu, Debasis & Kannan, Nandini & Balakrishnan, N., 2008. "On the hazard function of Birnbaum-Saunders distribution and associated inference," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2692-2702, January.
    4. Nadarajah, Saralees & Kotz, Samuel, 2006. "The beta exponential distribution," Reliability Engineering and System Safety, Elsevier, vol. 91(6), pages 689-697.
    5. Song, Peter X.K. & Fan, Yanqin & Kalbfleisch, John D., 2005. "Maximization by Parts in Likelihood Inference," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1145-1158, December.
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    1. Maha A. D. Aldahlan & Ahmed Z. Afify, 2020. "The Odd Exponentiated Half-Logistic Exponential Distribution: Estimation Methods and Application to Engineering Data," Mathematics, MDPI, vol. 8(10), pages 1-26, October.
    2. M. Elgarhy & Muhammad Ahsan Haq & Ismat Perveen, 2019. "Type II Half Logistic Exponential Distribution with Applications," Annals of Data Science, Springer, vol. 6(2), pages 245-257, June.
    3. Fiaz Ahmad Bhatti & G. G. Hamedani & Mustafa C. Korkmaz & Gauss M. Cordeiro & Haitham M. Yousof & Munir Ahmad, 2019. "On Burr III Marshal Olkin family: development, properties, characterizations and applications," Journal of Statistical Distributions and Applications, Springer, vol. 6(1), pages 1-21, December.
    4. Yaoting Yang & Weizhong Tian & Tingting Tong, 2021. "Generalized Mixtures of Exponential Distribution and Associated Inference," Mathematics, MDPI, vol. 9(12), pages 1-22, June.
    5. Sanku Dey & Mazen Nassar & Devendra Kumar, 2017. "$$\alpha $$ α Logarithmic Transformed Family of Distributions with Application," Annals of Data Science, Springer, vol. 4(4), pages 457-482, December.
    6. 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.
    7. Oseghale O. Innocent & Ayoola J. Femi & Oluwole Adegoke Nuga & Ogunde A. Adebisi, 2025. "Marshall-Olkin Extended Generalized Exponential Distribution: Properties, Inference and Application to Traffic Data," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 12(5), pages 1-1, January.
    8. Essam A. Ahmed, 2017. "Estimation and prediction for the generalized inverted exponential distribution based on progressively first-failure-censored data with application," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(9), pages 1576-1608, July.
    9. A. Nanthakumar, 2025. "A Copula Based Investigation of Reliability for the Multivariate Exponential Family of Distributions," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 12(4), pages 1-64, January.

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