PETSc version 3.17.0
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# PetscProbComputeKSStatistic

Compute the Kolmogorov-Smirnov statistic for the empirical distribution for an input vector, compared to an analytic CDF.

### Synopsis

    #include "petscdt.h"
    PetscErrorCode PetscProbComputeKSStatistic(Vec v, PetscProbFunc cdf, PetscReal *alpha)

Collective on v

### Input Parameters

| v | - The data vector, blocksize is the sample dimension
| cdf | - The analytic CDF

### Output Parameter

| 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.

### See Also

PetscProbFunc

### Level

advanced

### Location

src/dm/dt/interface/dtprob.c
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