Bias-Corrected Maximum Likelihood Estimation of the Parameters of the Modified Power Function Distribution

Abstract

One of the extended power function distributions is the modified power function distribution. It has a malleable probability distribution and may be used to represent bounded data on an interval (0,1). The maximum likelihood estimation (MLE) approach was used in the literature to estimate the distribution's parameters. However, because of the current prevalence of bias for a small sample size, this type of estimator has been widely warned. Consequently, we emphasize the method for reducing biased of the maximum likelihood estimators (MLEs) from order to . In addition, there are a bias-corrected approach (BCMLE) and a bootstrap approach (BOOT). Various scenarios in Monte Carlo simulations are proceeded to compare the effectiveness of estimators among MLEs, BCMLE, and BOOT methods. As a result, we found that the root mean square error of BCMLE is less than MLEs and BOOT. Similarly, when BCMLE MLEs and BOOT are applied to real datasets, the BSMLE has the smallest standard error. HIGHLIGHTS Focus on distribution for rates and proportions Elaborating both parametric and nonparametric methods Simulation study on various scenario GRAPHICAL ABSTRACT