改進Beta隨機變數之標準動差估計式

Improving Standard Moment Estimators of Beta Random Variables

第一類型貝塔分佈，包括兩個形狀參數，是學習統計學原理中古典動差方法的一種易於伸縮曲線設定。本文的研究源自計量經濟學之相似需要，進一步發現貝塔分佈具有一系列外顯高階動差估計式。除了對不同估計式進行加權試驗外，這項研究還考察了一個值得重視的情況，估計經典的四參數貝塔分佈，並允許動差方程替換。

The beta distribution of the first kind, including two shape parameters, is a flexible curve specification in studying the classical moment method of statistical principles. The research of this paper, originating with a need similar to that in econometrics, further finds a sequence of explicit high-order moment estimators for the beta distribution. In addition to the trials of weighting different moment estimators, this research also examines a deserving-emphasis condition for estimating the classic four-parameter beta distribution, and permitting moment-equation substitution.