Investigating the parameters of the beta distribution

The Beta distribution takes on many different shapes and may be described by two shape parameters, α and β, that can be difficult to estimate. Maximum likelihood and method of moments estimation are possible, though method of moments is much more straightforward and easier to compute by hand. In this paper, general information about the beta distribution were given. Usage areas of Beta distribution are also specified. The method of moment estimators and the system of linear equations of the maximum likelihood estimators are presented here. At the end of the investigation, it was discovered that the method of moment estimators is most preferable for small sample size (samples less than 50) whereas the Maximum Likelihood method is good when the sample size is large, this is because the estimates provided by this method are more consistent and asymptotically efficient; that is, they converge in probability to the parameter they are estimating and achieve the lower bound on variance.