我們使用伽瑪分配做為模型的假設，利用此分配能夠在分配假設不正確的情況之下，仍然能夠正確的估計母體平均數的特點，來製造新的適合度檢定統計量來檢定資料是否來自某一個特定的分配。本文將選用Kolmogorov-Smirnov (Kolmogorov,1933;Smirnov,1939)、Cramér–von Mises(Cramér,1928;von Mises,1931)與Anderson-Darling(1952)三個檢定統計量作比較。;We take advantage of the property that the gamma distribution is able to deliver consistent estimate for the mean parameter under model misspecification to develop a goodness of fit (GOF) test statistic. We use simulations to compare our novel test statistic with other GOF methods including the Kolmogorov-Smirnov、Cramér–von Mises and Anderson-Darling tests. It appears that our test outperforms in terms of testing power when the underlying distributions are similar to the null hypothesized distribution.
