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Statistical Properties and Different Methods of Estimation for Type I Half Logistic Inverted Kumaraswamy Distribution

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Deanship of Scientific Research, King AbdulAziz University, Jeddah 21589, Saudi Arabia
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Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt
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Department of Mathematics, Université de Caen, LMNO, Campus II, Science 3, 14032 Caen, France
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Department of Statistics, Govt. S.A Postgraduate College Dera Nawab Sahib, Bahawalpur, Punjab 63360, Pakistan
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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.
Mathematics 2019, 7(10), 1002; https://doi.org/10.3390/math7101002
Received: 23 September 2019 / Revised: 17 October 2019 / Accepted: 18 October 2019 / Published: 22 October 2019
(This article belongs to the Special Issue Probability, Statistics and their Applications)
In this paper, we introduce and study a new three-parameter lifetime distribution constructed from the so-called type I half-logistic-G family and the inverted Kumaraswamy distribution, naturally called the type I half-logistic inverted Kumaraswamy distribution. The main feature of this new distribution is to add a new tuning parameter to the inverted Kumaraswamy (according to the type I half-logistic structure), with the aim to increase the flexibility of the related inverted Kumaraswamy model and thus offering more precise diagnostics in data analyses. The new distribution is discussed in detail, exhibiting various mathematical and statistical properties, with related graphics and numerical results. An exhaustive simulation was conducted to investigate the estimation of the model parameters via several well-established methods, including the method of maximum likelihood estimation, methods of least squares and weighted least squares estimation, and method of Cramer-von Mises minimum distance estimation, showing their numerical efficiency. Finally, by considering the method of maximum likelihood estimation, we apply the new model to fit two practical data sets. In this regards, it is proved to be better than recent models, also derived to the inverted Kumaraswamy distribution. View Full-Text
Keywords: half-logistic distribution; inverted Kumaraswamy distribution; estimation methods; data analysis half-logistic distribution; inverted Kumaraswamy distribution; estimation methods; data analysis
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ZeinEldin, R.A.; Chesneau, C.; Jamal, F.; Elgarhy, M. Statistical Properties and Different Methods of Estimation for Type I Half Logistic Inverted Kumaraswamy Distribution. Mathematics 2019, 7, 1002.

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