Generating beta variates using several Monte-Carlo methods for estimating the distribution parameters .+CD

In this thesis, we consider the beta distribution with its important appearance in many statistical fields. Some mathematical and statistical properties of the distribution are illustrated and unified. Two methods of estimation "Moments method and Maximum Likelihood method" to the distribution parameters are discussed theoretically and assessed practically by utilizing five procedures of Monte-Carlo simulation for generating random varieties of the distribution. Efficiency of these procedures are found theoretically and compared practically. Comparisons between the two methods of estimation are made by using the mean square error measurement.