Study of a Modified Kumaraswamy Distribution

Rashad A. R. Bantan, Christophe Chesneau, Farrukh Jamal, Mohammed Elgarhy, Waleed Almutiry and Amani Abdullah Alahmadi
Additional contact information
Rashad A. R. Bantan: Department of Marine Geology, Faculty of Marine Science, King Abdulaziz University, Jeddah 21551, Saudi Arabia
Christophe Chesneau: Department of Mathematics, Campus II, Université de Caen Normandie, Science 3, 14032 Caen, France
Farrukh Jamal: Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan
Mohammed Elgarhy: The Higher Institute of Commercial Sciences, Al Mahalla Al Kubra, Al Gharbia 31951, Egypt
Waleed Almutiry: Department of Mathematics, College of Science and Arts in Ar Rass, Qassim University, Buryadah 52571, Saudi Arabia
Amani Abdullah Alahmadi: College of Science and Humanities, Shaqra University, Shaqra 15572, Saudi Arabia

Mathematics, 2021, vol. 9, issue 21, 1-26

Abstract: 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.

Keywords: Kumaraswamy distribution; logarithmic transformation; moments; quantile; real data applications (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/21/2836/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/21/2836/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:21:p:2836-:d:674697

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().