Investigating the parameters of the beta distribution
Department of Mathematics, University of Jos, Nigeria.
Research Article
World Journal of Advanced Research and Reviews, 2023, 19(01), 815–830
Article DOI: 10.30574/wjarr.2023.19.1.1409
Publication history:
Received on 04 June 2023; revised on 12 July 2023; accepted on 15 July 2023
Abstract:
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.
Keywords:
Estimator; Maximum Likelihood; Moments; Monograph; Mean Square Error
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