#include "petscdt.h" PetscErrorCode PetscProbComputeKSStatistic(Vec v, PetscProbFunc cdf, PetscReal *alpha)Collective on v
v | - The data vector, blocksize is the sample dimension | |
cdf | - The analytic CDF |
alpha | - The KS statisic |
Note: The Kolmogorov-Smirnov statistic for a given cumulative distribution function $F(x)$ is
D_n = \sup_x \left| F_n(x) - F(x) \right|
where $\sup_x$ is the supremum of the set of distances, and the empirical distribution function $F_n(x)$ is discrete, and given by
F_n = # of samples <= x / n
The empirical distribution function $F_n(x)$ is discrete, and thus had a ``stairstep'' cumulative distribution, making $n$ the number of stairs. Intuitively, the statistic takes the largest absolute difference between the two distribution functions across all $x$ values.