Some Properties of Skew Uniform Distribution

Salah H Abid^1,

¹Mathematics Department, Education College, Al-Mustansirya University, Baghdad, Iraq

Cite this paper

Salah H Abid. Some Properties of Skew Uniform Distribution. American Journal of Applied Mathematics and Statistics. 2015; 3(4):164-167. doi: 10.12691/AJAMS-3-4-6

Abstract

There is one work that appears to give some details of the skew uniform distribution, this work due to Aryal and Nadarajah [Random Operators and stochastic equations, Vol.12, No.4, pp.319-330, 2004]. They defined a random variable X to have the skew uniform distribution such that f_x(x)=2g(x)G(θx), where g(.) and G(.) denote the probability density function (pdf) and the cumulative distribution function (cdf) of the uniform distribution respectively. In this paper, we construct a new skewed distribution with pdf of the form 2f(x)G(θx), where θ is a real number, f(.) is taken to be uniform (-a,a) while G(.) comes from uniform (-b,b). We derive some properties of the new skewed distribution, the r th moment, mean, variance, skewness, kurtosis, moment generating function, characteristic function, hazard rate function, median, Rѐnyi entropy and Shannon entropy. We also consider the generating issues.

Keywords

Skew Uniform distribution, the r th moment, characteristic function, hazard rate function, Entropy

Copyright

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References

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