J型－發散統計量與數種適合度檢定統計量之比較

Abstract

Taneichi(1993)提出一個新的適合度檢定統計量J²，具有近似卡方分配的性質。然而在小樣本的情形下，計算機模擬結果顯示，它的估計顯著水準大於期望顯著水準。所以本論文的重點之一，就是對J²進行改進，根據不同的準則，來選取一個適當的常數a。我們建議對每一觀測次數加一常數0.32，作為我們修正後的統計量，這個統計量我們記為J₁²。

Taneichi(1993) introduces a new goodness-of-fit statisticJ², which has an asymptotic chi-squared distribution. However, the results of simulation indicate that the levels of significance are in general bigger than the nominal levels, which prompts us to device a version of J² statistic which would perform better under small sample size situations. We suggest adding 0.32 to each observed value and find that the adjustment indeed works rearonably well. This version of J^2 statistic is denoted as J(1)^2.