| 研究生: |
許惠婷 Hsu, Hui-Ting |
|---|---|
| 論文名稱: |
機率密度函數的峰數檢定之統計評估 Statistical Evaluation of Modality Tests of Probability Density Function |
| 指導教授: |
馬瀰嘉
Ma, Mi-Chia |
| 學位類別: |
碩士 Master |
| 系所名稱: |
管理學院 - 統計學系 Department of Statistics |
| 論文出版年: | 2008 |
| 畢業學年度: | 96 |
| 語文別: | 英文 |
| 論文頁數: | 58 |
| 中文關鍵詞: | Excess mass test 、Dip test 、峰數檢定 、Calibration 、Kolmogorov-Smirnov test 、檢定力 、單峰分配 |
| 外文關鍵詞: | Power, Modality test, Kolmogorov- Smirnov test, Calibration, Excess mass test, Unimodal distribution, Dip test |
| 相關次數: | 點閱:99 下載:1 |
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對於分配的多峰性檢定方法,過去已有多位學者提出,包含Dip test, Bandwidth test, Excess mass test,以及Cheng and Hall對Excess mass test 所做的修正方法等。這些方法的統計量大多與核密度函數估計有關,使得在計算上過於複雜且艱難。在研究過程中,我們發現多峰性檢定只要利用無母數方法Kolmogorov -Smirnov test即可簡便執行,利用與資料最相近的單峰分配之累積分配函數的最大差距作為統計量(與Dip test相似),當差距越大則表示此樣本離單峰分配越遠。此方法簡單易懂而且在軟體執行上也較為方便且快速。與過去學者提出的方法比較雖不及Cheng and Hall 的修正方法,但其檢定力在大樣本下勝於Dip test,且在實務上方便許多。最後,我們利用Single Nucleotide Polymorphism (SNP) 資料做為實例來說明。
Many methods were proposed to test the modality of probability density function in literatures, include the dip test, bandwidth test, and excess mass test. Cheng and Hall calibrated the excess mass test. Most of the test statistics of these methods were dependent on the estimation of kernel density function, so they were complicated and difficult on calculation. We use the adjusted Kolmogorov-Smirnov test of non- parametric method to test the modality. The statistic is the maximum difference between the empirical distribution function and the most close unimodal distribution function. The spirit of this method is similar to the dip test. The maximum difference is larger if the sample is far from the unimodal distribution. This method is straightforward and easy to compute and more convenient by current statistical package. A simulation study is conducted to compare these methods. The simulation results show that the power of the adjusted Kolmogorov-Smirnov test is greater than that of the dip test for large sample size, but less than that of Cheng and Hall. Finally, a Single Nucleotide Polymorphism (SNP) data is illustrated to explain.
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