在次序統計量下以加權最小平方估算分配函數之參數

An Alternative Method Estimate the Parameter of the Distribution by Order Statistics

本文主要提出一個加權最小平方法(weighted least square estimation: WLSE)去估算具二個參數分配函數之參數，且對指數分布、極值分布、對數常態分布、邏輯斯分布等分布，根據可被觀察資料的位置，給予適當的加權因子。利用次序統計量提出不同的加權權重因子。並以邏輯斯分布為例，模疑WLSE與OLSE、AMLE效能之比較。結果顯示，對不同二個參數之估算，WLSE都比OLSE精確。但對第1個參數之估算，WLSE都比AMLE差，但仍在5%以內；對第2個參數之估算，WLSE則與AMLE無明顯差異。

In this article, we propose a weighted least square method (WLSE) to estimate the parameters of the two-parameter distributions, which are widely used in, for example, Exponential, Extreme-Value, Linear exponential, Lognormal and Logistic distributions etc.. In our approach, suitable weighting factors are provided based on the locations of the sorted observable data. We also demonstrated the comparisons of efficiency among simulated XML SE, ordinary least square estimation (OLSE) and approximate maximum likelihood estimation (AMLE) using Logistic distributions. The results show that for the estimation of the two parameters, WLSE is much more precise than OLSE. However, for the estimation of first parameter, WLSE is worse than ANILE but still within 5%. For the estimation of the second parameter, there is no significant difference between WLSE and AMLE.