The Kumaraswamy Exponentiated U-Quadratic Distribution: Properties and Application

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Mustapha Muhammad
Isyaku Muhammad
Aisha Muhammad Yaya


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.

Kumaraswamy-G distribution, exponentiated U-qadrtic distribution, moments, maximum likelihood estimation

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How to Cite
Muhammad, M., Muhammad, I., & Muhammad Yaya, A. (2018). The Kumaraswamy Exponentiated U-Quadratic Distribution: Properties and Application. Asian Journal of Probability and Statistics, 1(3), 1-17.
Original Research Article