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Type II Power Topp-Leone Generated Family of Distributions with Statistical Inference and 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.
Symmetry 2020, 12(1), 75; https://doi.org/10.3390/sym12010075
Received: 14 November 2019 / Revised: 22 December 2019 / Accepted: 25 December 2019 / Published: 2 January 2020
In this paper, we present and study a new family of continuous distributions, called the type II power Topp-Leone-G family. It provides a natural extension of the so-called type II Topp-Leone-G family, thanks to the use of an additional shape parameter. We determine the main properties of the new family, showing how they depend on the involving parameters. The following points are investigated: shapes and asymptotes of some important functions, quantile function, some mixture representations, moments and derivations, stochastic ordering, reliability and order statistics. Then, a special model of the family based on the inverse exponential distribution is introduced. It is of particular interest because the related probability functions are tractable and possess various kinds of asymmetric shapes. Specially, reverse J, left skewed, near symmetrical and right skewed shapes are observed for the corresponding probability density function. The estimation of the model parameters is performed by the use of three different methods. A complete simulation study is proposed to illustrate their numerical efficiency. The considered model is also applied to analyze two different kinds of data sets. We show that it outperforms other well-known models defined with the same baseline distribution, proving its high level of adaptability in the context of data analysis. View Full-Text
Keywords: Topp-Leone distribution; type II Topp-Leone-G family; moments; stochastic ordering; reliability; estimation; data analysis Topp-Leone distribution; type II Topp-Leone-G family; moments; stochastic ordering; reliability; estimation; data analysis
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Bantan, R.A.R.; Jamal, F.; Chesneau, C.; Elgarhy, M. Type II Power Topp-Leone Generated Family of Distributions with Statistical Inference and Applications. Symmetry 2020, 12, 75.

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