基於兩樣本Bootstrap檢驗的伽瑪分佈變異係數多重比較檢驗

Multiple Comparison Test of Coefficient of Variation of Gamma Distribution Based on Two-Sample Bootstrap Test

江海紅(Hai-Hong Jiang)；金百鎖(Bai-Suo Jin)

伽瑪分佈 ； 閉型估計量 ； 變異係數 ； Bootstrap ； 多重比較檢驗 ； 功效 ； gamma distribution ； closed-form estimators ； coefficient of variation ； Bootstrap ； multiple comparison test ； power

中國統計學報

58卷4期（2020 / 12 / 01）

294 - 311

繁體中文

伽瑪分佈是一種流行的分佈模型，適用於右偏數據建模，在氣候學、金融和環境科學等領域有廣泛應用。伽瑪分佈閉型估計量是由廣義伽瑪分佈似然方程推導出的估計量（Ye＆Chen, 2017）。本文在閉型估計量基礎上構造兩樣本Bootstrap檢驗並通過混合過程（Hybrid procedure）逐步向上方法進行伽瑪分佈變異係數多重比較檢驗。在三樣本下進行變異係數多重檢驗功效模擬，模擬結果表明檢驗方法是可行的；實證分析採用了美國匹茲堡市9個市議會區在2008年至2013年共72個月裡重罪和輕罪的犯罪次數，以及2015年至2019年安徽省12個地級市月平均PM2.5濃度數據，進一步驗證了該檢驗方法的適用性。

The gamma distribution is a popular distribution model, which is suitable for modeling data with right-skewness and is widely used in climatology, finance and environmental science. The closed-form estimators for the gamma distribution are derived from the likelihood equations of generalized gamma distribution by Ye and Chen (Ye & Chen, 2017). In this paper, the two-sample bootstrap test is used on the basis of closed-form estimators, and then the hybrid procedure step-up procedure is used to carry out the multiple comparison test of the coefficient of variation of gamma distribution. The power simulation of multiple test for equality of coefficient of variation was carried out under three-sample, and the simulation results show that the test method is feasible. The empirical analysis used the number of serious crime and misdemeanor committed in the total of 72 months from 2008 to 2013 in nine city council districts in Pittsburgh and the average monthly PM2.5 concentration data from 2015 to 2019 in 12 cities in Anhui province, which further verified the applicability of the test method.

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