The Kumaraswamy Exponentiated U-Quadratic Distribution: Properties and Application
Mustapha Muhammad *
Department of Mathematical Sciences, Bayero University Kano, Nigeria
Isyaku Muhammad
Department of Mechanical Engineering, School of Technology, Kano State Polytechnic, Nigeria
Aisha Muhammad Yaya
Department of Mathematical Sciences, Bayero University Kano, Nigeria
*Author to whom correspondence should be addressed.
Abstract
In this paper, a new lifetime model called Kumaraswamy exponentiated U-quadratic (KwEUq) distribution is proposed. Several mathematical and statistical properties are derived and studied such as the explicit form of the quantile function, moments, moment generating function, order statistics, probability weighted moments, Shannon entropy and Renyi entropy. We also found that the usual maximum likelihood estimates (MLEs) fail to hold for the KwEUq distribution. Two alternative methods are suggested for the parameter estimation of the KwEUq, the alternative maximum likelihood estimation (AMLE) and modified maximum likelihood estimation (MMLE). Simulation studies were conducted to assess the finite sample behavior of the AMLEs and MMLEs. Finally, we provide application of the KwEUq for illustration purposes.
Keywords: Kumaraswamy-G distribution, exponentiated U-qadrtic distribution, moments, maximum likelihood estimation