Compared Methods of Generating Both Gamma Distribution and Beta Distribution

	Compared Methods of Generating Both Gamma Distribution and Beta Distribution
journal of Economics And Administrative Sciences/ University of baghdad
Article 1, Volume 19, Issue 72, 2013, Pages 214-242
Abstract
Gamma and Beta Distributions has very important in practice in various areas of statistical and applications reliability and quality control of production. and There are a number of methods to generate data behave on according to these distribution. and These methods bassic primarily on the shape parameters of each distribution and the relationship between these distributions and their relationship with some other probability distributions. This research aims to determine how most efficient method for generating gamma varieties upon the shape parameter α and generating beta varieties upon the two shape parameters α, β. The common comparison between the methods of generating random variables computerized rely on the less number of random numbers , as well as the time it takes to generate a single value of a random variable x, regardless of statistical efficiency. In this paper and for the first time,we used the mean square error MSE of the mean and the varianes of the samples that have been generated for the different sizes of the samples as the statistical comparison. As well as a proposal of two methods to generate data distributed according to beta distribution using the least number of random numbers and the highest ef-ficiency. We prove by running a number of simulation experiments, programs written by researcher used MATLAB language.
Keywords
Gamma distribution; Beta Distribution; random variables; Generating; Simulation; gamma

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