Distribution Fitters

[rwilcox]

I´ve been hearing about chi-squared, Kolmogorov-Smirnov, and Anderson-Darling goodness-of-fit tests for fitting theoretical distributions to empirical data. What are their similarities, differences, advantages, and disadvantages?

[ewilliams]

The Kolmogorov-Smirnov and the Anderson-Darling tests both examine the closeness of fit of the empirical distribution to the candidate closed-form distribution. The K-S test (as it is often abbreviated) calculates the maximum value of the absolute value of the difference between the two distribution functions. The Anderson-Darling test integrates the integral of the difference-squared between the two distribution functions, multiplied by a weighting function. This modification means that the A-D test (as it's often abbreviated) gives more importance to good fit in the tails -- where the simulation modeler's interest often focuses in practice.