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A New Power Topp–Leone Generated Family of Distributions with Applications

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Department of Marine Geology, Faculty of Marine Sience, King AbdulAziz University, Jeddah 21551, Saudi Arabia
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Deanship of Scientific Research, King AbdulAziz University, Jeddah 21551, Saudi Arabia
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Department of Statistics, Govt. S.A Postgraduate College Dera Nawab Sahib, Bahawalpur, Punjab 63100, Pakistan
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Department of Mathematics, Université de Caen, LMNO, Campus II, Science 3, 14032 Caen, France
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Valley High Institute for Management Finance and Information Systems, Obour, Qaliubia 11828, Egypt
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Author to whom correspondence should be addressed.
Entropy 2019, 21(12), 1177; https://doi.org/10.3390/e21121177
Received: 12 November 2019 / Revised: 24 November 2019 / Accepted: 28 November 2019 / Published: 29 November 2019
In this paper, we introduce a new general family of distributions obtained by a subtle combination of two well-established families of distributions: the so-called power Topp–Leone-G and inverse exponential-G families. Its definition is centered around an original cumulative distribution function involving exponential and polynomial functions. Some desirable theoretical properties of the new family are discussed in full generality, with comprehensive results on stochastic ordering, quantile function and related measures, general moments and related measures, and the Shannon entropy. Then, a statistical parametric model is constructed from a special member of the family, defined with the use of the inverse Lomax distribution as the baseline distribution. The maximum likelihood method was applied to estimate the unknown model parameters. From the general theory of this method, the asymptotic confidence intervals of these parameters were deduced. A simulation study was conducted to evaluate the numerical behavior of the estimates we obtained. Finally, in order to highlight the practical perspectives of the new family, two real-life data sets were analyzed. All the measures considered are favorable to the new model in comparison to four serious competitors. View Full-Text
Keywords: power Topp–Leone distribution; inverse exponential-G family; moments; entropy; estimation; data analysis power Topp–Leone distribution; inverse exponential-G family; moments; entropy; estimation; data analysis
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Bantan, R.A.R.; Jamal, F.; Chesneau, C.; Elgarhy, M. A New Power Topp–Leone Generated Family of Distributions with Applications. Entropy 2019, 21, 1177.

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