kstests.c File Reference

Perform the Kolmogorov-Smirnov test for two sets of samples. More...

#include "mdb.h"
#include "sort.h"

Go to the source code of this file.

Macros
#define	KS_Q_ACCURACY   1e-8
#define	KS_Q_MAXTERMS   1000

Functions
double	twoVariableKStest (double *d1, long n1, double *d2, long n2, double *maxCDFerror)
double	KS_Qfunction (double lambda)
	Compute the Q-function for the Kolmogorov-Smirnov test.

Detailed Description

Perform the Kolmogorov-Smirnov test for two sets of samples.

Copyright

• (c) 2002 The University of Chicago, as Operator of Argonne National Laboratory.
• (c) 2002 The Regents of the University of California, as Operator of Los Alamos National Laboratory.

License

This file is distributed under the terms of the Software License Agreement found in the file LICENSE included with this distribution.

Author

M. Borland, C. Saunders, R. Soliday

Definition in file kstests.c.

Macro Definition Documentation

KS_Q_ACCURACY

#define KS_Q_ACCURACY   1e-8

Definition at line 45 of file kstests.c.

KS_Q_MAXTERMS

#define KS_Q_MAXTERMS   1000

Definition at line 46 of file kstests.c.

Function Documentation

KS_Qfunction()

double KS_Qfunction

(

double

lambda

)

Compute the Q-function for the Kolmogorov-Smirnov test.

Given a lambda value, this function approximates the complementary cumulative distribution function needed to determine the KS probability (Q-value).

Parameters

lambda

The computed KS statistic scaled by sqrt(N).

Returns

The KS Q-value as a probability measure.

Definition at line 57 of file kstests.c.

                                   {
  long j;
  double expFactor, factor;
  double sum, term;
 
  expFactor = -2 * lambda * lambda;
  factor = 1;
  j = 1;
  sum = 0;
  do {
    term = exp(expFactor * j * j);
    sum += factor * term;
    factor *= -1;
  } while (term > KS_Q_ACCURACY && j++ < KS_Q_MAXTERMS);
  if (j > KS_Q_MAXTERMS)
    fputs("warning: KS test did not converge\n", stderr);
  return 2 * sum;
}

twoVariableKStest()

double twoVariableKStest	(	double *	d1,
		long	n1,
		double *	d2,
		long	n2,
		double *	maxCDFerror )

Definition at line 19 of file kstests.c.

                                                                                        {
  long i1, i2;
  double CDFerror, xDifference, CDF1, CDF2, sqrtNe;
 
  qsort((void *)d1, n1, sizeof(*d1), double_cmpasc);
  qsort((void *)d2, n2, sizeof(*d2), double_cmpasc);
  i1 = i2 = 0;
  CDF1 = CDF2 = 0;
  *maxCDFerror = 0;
  while (i1 < n1 && i2 < n2) {
    /* move through the arrays together, keeping value from both arrays as close as possible.
           xDifference is the distance between the points at which the CDFs are evaluated.
         */
    if ((xDifference = d1[i1] - d2[i2]) <= 0)
      /* d2 is evaluated ahead of d1, so advance d1 */
      CDF1 = ++i1 / ((double)n1);
    if (xDifference >= 0)
      /* d1 is evaluated ahead of d2 */
      CDF2 = ++i2 / ((double)n2);
    if ((CDFerror = fabs(CDF1 - CDF2)) > *maxCDFerror)
      *maxCDFerror = CDFerror;
  }
  sqrtNe = sqrt(((double)n1 * n2) / ((double)n1 + n2));
  return KS_Qfunction((sqrtNe + 0.12 + 0.11 / sqrtNe) * (*maxCDFerror));
}