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Roussas, G. (2014). “A Course in Mathematical Statistics” , third edition, Academic Press.

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Article

Some Properties of Skew Uniform Distribution

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


American Journal of Applied Mathematics and Statistics. 2015, Vol. 3 No. 4, 164-167
DOI: 10.12691/ajams-3-4-6
Copyright © 2015 Science and Education Publishing

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.

Correspondence to: Salah  H Abid, Mathematics Department, Education College, Al-Mustansirya University, Baghdad, Iraq. Email: abidsalah@gmail.com

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 fx(x)=2g(x)Gx), 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)Gx), 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.

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