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Open AccessArticle

Type II Topp–Leone Inverted Kumaraswamy Distribution with Statistical Inference and Applications

1
Deanship of Scientific Research, King AbdulAziz University, Jeddah 21589, Saudi Arabia
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Faculty of Graduate Studies for Statistical Research, Cairo University, Al Orman, Giza Governorate 12613, 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, Caen 14032, France
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Valley High Institute for Management Finance and Information Systems, Obour, Qaliubia 11828, Egypt
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(12), 1459; https://doi.org/10.3390/sym11121459
Received: 5 November 2019 / Revised: 20 November 2019 / Accepted: 26 November 2019 / Published: 28 November 2019
In this paper, we present and study a new four-parameter lifetime distribution obtained by the combination of the so-called type II Topp–Leone-G and transmuted-G families and the inverted Kumaraswamy distribution. By construction, the new distribution enjoys nice flexible properties and covers some well-known distributions which have already proven themselves in statistical applications, including some extensions of the Bur XII distribution. We first present the main functions related to the new distribution, with discussions on their shapes. In particular, we show that the related probability density function is left, right skewed, near symmetrical and reverse J shaped, with a notable difference regarding the right tailed, illustrating the flexibility of the distribution. Then, the related model is displayed, with the estimation of the parameters by the maximum likelihood method and the consideration of two practical data sets. We show that the proposed model is the best one in terms of standard model selection criteria, including Akaike information and Bayesian information criteria, and goodness of fit tests against three well-established competitors. Then, for the new model, the theoretical background on the maximum likelihood method is given, with numerical guaranties of the efficiency of the estimates obtained via a simulation study. Finally, the main mathematical properties of the new distribution are discussed, including asymptotic results, quantile function, Bowley skewness and Moors kurtosis, mixture representations for the probability density and cumulative density functions, ordinary moments, incomplete moments, probability weighted moments, stress-strength reliability and order statistics. View Full-Text
Keywords: type II Topp–Leone distribution; inverted Kumaraswamy distribution; estimation; simulation; data analysis type II Topp–Leone distribution; inverted Kumaraswamy distribution; estimation; simulation; data analysis
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ZeinEldin, R.A.; Jamal, F.; Chesneau, C.; Elgarhy, M. Type II Topp–Leone Inverted Kumaraswamy Distribution with Statistical Inference and Applications. Symmetry 2019, 11, 1459.

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