The Marshall-Olkin logistic-exponential distribution |
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| Authors: | M Mansoor M H Tahir Gauss M Cordeiro Serge B Provost Ayman Alzaatreh |
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| Institution: | 1. Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur, Pakistan;2. Department of Statistics, Federal University of Pernambuco, Recife, PE, Brazil;3. Department of Statistical and Actuarial Sciences, The University of Western Ontario, London, Canada;4. Department of Mathematics and Statistics, American University of Sharjah, Sharjah, UAE |
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| 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. |
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| Keywords: | Censored data Logistic distribution Logistic-exponential distribution Marshall-Olkin family Maximum likelihood estimation |
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