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Open AccessArticle

The Exponentiated Truncated Inverse Weibull-Generated Family of Distributions with Applications

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Statistics Department, Faculty of Science, King AbdulAziz University, Jeddah 21551, Saudi Arabia
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Valley High Institute for Management Finance and Information Systems, Obour, Qaliubia 11828, Egypt
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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
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(4), 650; https://doi.org/10.3390/sym12040650
Received: 16 March 2020 / Revised: 9 April 2020 / Accepted: 13 April 2020 / Published: 20 April 2020
In this paper, we propose a generalization of the so-called truncated inverse Weibull-generated family of distributions by the use of the power transform, adding a new shape parameter. We motivate this generalization by presenting theoretical and practical gains, both consequences of new flexible symmetric/asymmetric properties in a wide sense. Our main mathematical results are about stochastic ordering, uni/multimodality analysis, series expansions of crucial probability functions, probability weighted moments, raw and central moments, order statistics, and the maximum likelihood method. The special member of the family defined with the inverse Weibull distribution as baseline is highlighted. It constitutes a new four-parameter lifetime distribution which brightensby the multitude of different shapes of the corresponding probability density and hazard rate functions. Then, we use it for modelling purposes. In particular, a complete numerical study is performed, showing the efficiency of the corresponding maximum likelihood estimates by simulation work, and fitting three practical data sets, with fair comparison to six notable models of the literature. View Full-Text
Keywords: truncated family of distributions; inverse Weibull distribution; moments; order statistics; maximum likelihood method; simulation; data analysis truncated family of distributions; inverse Weibull distribution; moments; order statistics; maximum likelihood method; simulation; data analysis
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MDPI and ACS Style

Almarashi, A.M.; Elgarhy, M.; Jamal, F.; Chesneau, C. The Exponentiated Truncated Inverse Weibull-Generated Family of Distributions with Applications. Symmetry 2020, 12, 650.

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