Dept of Bioenvironmental Systems EngineeringNational Taiwan University

Lab for Remote Sensing Hydrology and Spatial

Modeling

Goodness-of-fit Tests

Chi-Square GOF testKolmogorov-Smirnov GOF test

Professor Ke-Sheng ChengDepartment of Bioenvironmental Systems

EngineeringNational Taiwan University

Lab for Remote Sensing Hydrology and Spatial Modeling

Dept of Bioenvironmental Systems EngineeringNational Taiwan University

Chi-square GOF test Concept

Lab for Remote Sensing Hydrology and Spatial Modeling

Dept of Bioenvironmental Systems EngineeringNational Taiwan University

Chi-square GOF test

Lab for Remote Sensing Hydrology and Spatial Modeling

Dept of Bioenvironmental Systems EngineeringNational Taiwan University

Lab for Remote Sensing Hydrology and Spatial Modeling

Dept of Bioenvironmental Systems EngineeringNational Taiwan University

Lab for Remote Sensing Hydrology and Spatial Modeling

Dept of Bioenvironmental Systems EngineeringNational Taiwan University

Lab for Remote Sensing Hydrology and Spatial Modeling

Dept of Bioenvironmental Systems EngineeringNational Taiwan University

Lab for Remote Sensing Hydrology and Spatial Modeling

Dept of Bioenvironmental Systems EngineeringNational Taiwan University

Lab for Remote Sensing Hydrology and Spatial Modeling

Dept of Bioenvironmental Systems EngineeringNational Taiwan University

Lab for Remote Sensing Hydrology and Spatial Modeling

Dept of Bioenvironmental Systems EngineeringNational Taiwan University

Kolmogorov-Smirnov GOF testConcept

Lab for Remote Sensing Hydrology and Spatial Modeling

Dept of Bioenvironmental Systems EngineeringNational Taiwan University

Kolmogorov-Smirnov GOF test The chi-square test compares the

empirical histogram against the theoretical histogram.

In contrast, the K-S test compares the empirical cumulative distribution function (ECDF) against the theoretical CDF.

Lab for Remote Sensing Hydrology and Spatial Modeling

Dept of Bioenvironmental Systems EngineeringNational Taiwan University

Lab for Remote Sensing Hydrology and Spatial Modeling

Dept of Bioenvironmental Systems EngineeringNational Taiwan University

Lab for Remote Sensing Hydrology and Spatial Modeling

Dept of Bioenvironmental Systems EngineeringNational Taiwan University

Lab for Remote Sensing Hydrology and Spatial Modeling

Dept of Bioenvironmental Systems EngineeringNational Taiwan University

In order to measure the difference between Fn(X) and F(X), ECDF statistics based

on the vertical distances between Fn(X) a

nd F(X) have been proposed.

Lab for Remote Sensing Hydrology and Spatial Modeling

Dept of Bioenvironmental Systems EngineeringNational Taiwan University

Lab for Remote Sensing Hydrology and Spatial Modeling

Dept of Bioenvironmental Systems EngineeringNational Taiwan University

Lab for Remote Sensing Hydrology and Spatial Modeling

Dept of Bioenvironmental Systems EngineeringNational Taiwan University

Lab for Remote Sensing Hydrology and Spatial Modeling

Dept of Bioenvironmental Systems EngineeringNational Taiwan University

Lab for Remote Sensing Hydrology and Spatial Modeling

Dept of Bioenvironmental Systems EngineeringNational Taiwan University

Lab for Remote Sensing Hydrology and Spatial Modeling

Dept of Bioenvironmental Systems EngineeringNational Taiwan University

Lab for Remote Sensing Hydrology and Spatial Modeling

Dept of Bioenvironmental Systems EngineeringNational Taiwan University

Lab for Remote Sensing Hydrology and Spatial Modeling

Dept of Bioenvironmental Systems EngineeringNational Taiwan University

Values of for the Kolmogorov-Smirnov test

,nD