Estimation of Shape β Parameter in Kumaraswamy Distribution Using Maximum Likelihood and Bayes Method

摘要

This paper discusses the Maximum Likelihood (ML) and Bayes method for estimating the shape β parameter in Kumaraswamy distribution. Both methods will be compared according to Mean Square Error (MSE) obtained from each estimator. In the Bayes method, two Loss functions will be used, i.e., the Square Error Loss Function (SELF) and Precautionary Loss Function (PLF). Then, the Posterior Risk obtained from both loss functions will be compared. The comparison will be applied to hydrological data as a recommendation for the best method of representing the data. Hydrological data used in this study is a water storage in Shasta Reservoir, obtained from the California Data Exchange Center. By using the Mathematica Software and the formulas from both methods one obtains a statistic which can nicely describe the data and also predict the next observation of a reservoir in a certain time.