1. Kolmogorov-Smirnov GOF test
The chi-square test compares the empirical histogram against the theoretical histogram.
By contrast, the K-S test compares the empirical cumulative distribution function (ECDF) against the theoretical CDF.
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Lab for Remote Sensing Hydrology and Spatial Modeling, Dept. of Bioenvironmental Systems Eng., NTU

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Lab for Remote Sensing Hydrology and Spatial Modeling, Dept. of Bioenvironmental Systems Eng., NTU

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Lab for Remote Sensing Hydrology and Spatial Modeling, Dept. of Bioenvironmental Systems Eng., NTU

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Lab for Remote Sensing Hydrology and Spatial Modeling, Dept. of Bioenvironmental Systems Eng., NTU

5. In order to measure the difference between Fn(X) and F(X), ECDF statistics based on the vertical distances between Fn(X) and F(X) have been proposed.
1/28/2020
Lab for Remote Sensing Hydrology and Spatial Modeling, Dept. of Bioenvironmental Systems Eng., NTU

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Lab for Remote Sensing Hydrology and Spatial Modeling, Dept. of Bioenvironmental Systems Eng., NTU

7. Stochastic convergence Almost-sure convergence or
Convergence with probability 1
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Lab for Remote Sensing Hydrology and Spatial Modeling, Dept. of Bioenvironmental Systems Eng., NTU

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Lab for Remote Sensing Hydrology and Spatial Modeling, Dept. of Bioenvironmental Systems Eng., NTU

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Lab for Remote Sensing Hydrology and Spatial Modeling, Dept. of Bioenvironmental Systems Eng., NTU

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Lab for Remote Sensing Hydrology and Spatial Modeling, Dept. of Bioenvironmental Systems Eng., NTU

11. Hypothesis test using Dn
1/28/2020
Lab for Remote Sensing Hydrology and Spatial Modeling, Dept. of Bioenvironmental Systems Eng., NTU

12. Values of for the Kolmogorov-Smirnov test
1/28/2020
Lab for Remote Sensing Hydrology and Spatial Modeling, Dept. of Bioenvironmental Systems Eng., NTU

13. Interpretation of the probability distribution of the test statistic
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Lab for Remote Sensing Hydrology and Spatial Modeling, Dept. of Bioenvironmental Systems Eng., NTU

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Lab for Remote Sensing Hydrology and Spatial Modeling, Dept. of Bioenvironmental Systems Eng., NTU