Study of a Modified Kumaraswamy Distribution

Mathematics

Amani Abdullah Alahmadi¹  Rashad A. R. Bantan²  Christophe Chesneau³  Waleed Almutiry⁴  Farrukh Jamal⁵  Mohammed Elgarhy⁶ 

[1] College of Science and Humanities, Shaqra University, Shaqra 15572, Saudi Arabia;Department of Marine Geology, Faculty of Marine Science, King Abdulaziz University, Jeddah 21551, Saudi Arabia;Department of Mathematics, Campus II, Université de Caen Normandie, Science 3, 14032 Caen, France;Department of Mathematics, College of Science and Arts in Ar Rass, Qassim University, Buryadah 52571, Saudi Arabia;Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan;The Higher Institute of Commercial Sciences, Al Mahalla Al Kubra, Al Gharbia 31951, Egypt;

关键词: Kumaraswamy distribution;    logarithmic transformation;    moments;    quantile;    real data applications;   

DOI  :  10.3390/math9212836

来源: DOAJ

【 摘 要 】

In this article, a structural modification of the Kumaraswamy distribution yields a new two-parameter distribution defined on $(0,1)$, called the modified Kumaraswamy distribution. It has the advantages of being (i) original in its definition, mixing logarithmic, power and ratio functions, (ii) flexible from the modeling viewpoint, with rare functional capabilities for a bounded distribution—in particular, N-shapes are observed for both the probability density and hazard rate functions—and (iii) a solid alternative to its parental Kumaraswamy distribution in the first-order stochastic sense. Some statistical features, such as the moments and quantile function, are represented in closed form. The Lambert function and incomplete beta function are involved in this regard. The distributions of order statistics are also explored. Then, emphasis is put on the practice of the modified Kumaraswamy model in the context of data fitting. The well-known maximum likelihood approach is used to estimate the parameters, and a simulation study is conducted to examine the performance of this approach. In order to demonstrate the applicability of the suggested model, two real data sets are considered. As a notable result, for the considered data sets, statistical benchmarks indicate that the new modeling strategy outperforms the Kumaraswamy model. The transmuted Kumaraswamy, beta, unit Rayleigh, Topp–Leone and power models are also outperformed.

【 授权许可】

Unknown