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Open AccessArticle

Truncated Inverted Kumaraswamy Generated Family of Distributions with Applications

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Deanship of Scientific Research, King Abdulaziz University, Jeddah 21442, 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(11), 1089; https://doi.org/10.3390/e21111089
Received: 21 October 2019 / Revised: 1 November 2019 / Accepted: 5 November 2019 / Published: 7 November 2019
In this article, we introduce a new general family of distributions derived to the truncated inverted Kumaraswamy distribution (on the unit interval), called the truncated inverted Kumaraswamy generated family. Among its qualities, it is characterized with tractable functions, has the ability to enhance the flexibility of a given distribution, and demonstrates nice statistical properties, including competitive fits for various kinds of data. A particular focus is given on a special member of the family defined with the exponential distribution as baseline, offering a new three-parameter lifetime distribution. This new distribution has the advantage of having a hazard rate function allowing monotonically increasing, decreasing, and upside-down bathtub shapes. In full generality, important properties of the new family are determined, with an emphasis on the entropy (Rényi and Shannon entropy). The estimation of the model parameters is established by the maximum likelihood method. A numerical simulation study illustrates the nice performance of the obtained estimates. Two practical data sets are then analyzed. We thus prove the potential of the new model in terms of fitting, with favorable results in comparison to other modern parametric models of the literature. View Full-Text
Keywords: inverted Kumaraswamy distribution; truncated distribution; moments; entropy; maximum likelihood estimation; simulation; data analysis inverted Kumaraswamy distribution; truncated distribution; moments; entropy; maximum likelihood estimation; simulation; data analysis
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Bantan, R.A.R.; Jamal, F.; Chesneau, C.; Elgarhy, M. Truncated Inverted Kumaraswamy Generated Family of Distributions with Applications. Entropy 2019, 21, 1089.

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