On the skew uniform distribution

A random variable X is said to have the skew-uniform distribution if its pdf is ƒ(x) = 2g(x)G(λx), where g(·) and G(·), respectively, denote the pdf and the cdf of the Uniform (−θ, θ) distribution. This distribution – in spite of its simplicity – appears not to have been studied in detail. The only work that appears to give some details of this distribution is Gupta et al. [Random Operators and Stochastic Equations, 10, 2002, 133–140], where expressions for the pdf, moment generating function, expectation, variance, skewness and the kurtosis of X are given. Unfortunately, all of these expressions appear to contain some errors. In this paper, we provide a comprehensive description of the mathematical properties of X. The properties derived include the kth moment, the kth central moment, variance, skewness, kurtosis, moment generating function, characteristic function, hazard rate function, mean deviation about the mean, mean deviation about the median, Rényi entropy, Shannon entropy and the asymptotic distribution of the extreme order statistics. We also consider estimation and simulation issues.