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SUBROUTINE KOLM2

PURPOSE

   TESTS THE DIFFERENCE BETWEEN TWO SAMPLE DISTRIBUTION
   FUNCTIONS USING THE KOLMOGOROV-SMIRNOV TEST

USAGE
   CALL KOLM2(X,Y,N,M,Z,PROB)

DESCRIPTION OF PARAMETERS
   X	- INPUT VECTOR OF N INDEPENDENT OBSERVATIONS.  ON
	  RETURN FROM KOLM2, X HAS BEEN SORTED INTO A
	  MONOTONIC NON-DECREASING SEQUENCE.
   Y	- INPUT VECTOR OF M INDEPENDENT OBSERVATIONS.  ON
	  RETURN FROM KOLM2, Y HAS BEEN SORTED INTO A
	  MONOTONIC NON-DECREASING SEQUENCE.
   N	- NUMBER OF OBSERVATIONS IN X
   M	- NUMBER OF OBSERVATIONS IN Y
   Z	- OUTPUT VARIABLE CONTAINING THE GREATEST VALUE WITH
	  RESPECT TO THE SPECTRUM OF X AND Y OF
	  SQRT((M*N)/(M+N))*ABS(FN(X)-GM(Y)) WHERE
	  FN(X) IS THE EMPIRICAL DISTRIBUTION FUNCTION OF THE
	  SET (X) AND GM(Y) IS THE EMPIRICAL DISTRIBUTION
	  FUNCTION OF THE SET (Y).
   PROB - OUTPUT VARIABLE CONTAINING THE PROBABILITY OF
	  THE STATISTIC BEING GREATER THAN OR EQUAL TO Z IF
	  THE HYPOTHESIS THAT X AND Y ARE FROM THE SAME PDF IS
	  TRUE.  E.G., PROB= 0.05 IMPLIES THAT ONE CAN REJECT
	  THE NULL HYPOTHESIS THAT THE SETS X AND Y ARE FROM
	  THE SAME DENSITY WITH 5 PER CENT PROBABILITY OF BEING
	  INCORRECT.  PROB = 1. - SMIRN(Z).

REMARKS
   N AND M SHOULD BE GREATER THAN OR EQUAL TO 100.  (SEE THE
   MATHEMATICAL DESCRIPTION FOR THIS SUBROUTINE AND FOR THE
   SUBROUTINE SMIRN, CONCERNING ASYMPTOTIC FORMULAE).

   DOUBLE PRECISION USAGE---IT IS DOUBTFUL THAT THE USER WILL
   WISH TO PERFORM THIS TEST USING DOUBLE PRECISION ACCURACY.
   IF ONE WISHES TO COMMUNICATE WITH KOLM2 IN A DOUBLE
   PRECISION PROGRAM, HE SHOULD CALL THE FORTRAN SUPPLIED
   PROGRAM SNGL(X) PRIOR TO CALLING KOLM2, AND CALL THE
   FORTRAN SUPPLIED PROGRAM DBLE(X) AFTER EXITING FROM KOLM2.
   (NOTE THAT SUBROUTINE SMIRN DOES HAVE DOUBLE PRECISION
   CAPABILITY AS SUPPLIED BY THIS PACKAGE.)


SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   SMIRN

METHOD
   FOR REFERENCE, SEE (1) W. FELLER--ON THE KOLMOGOROV-SMIRNOV
   LIMIT THEOREMS FOR EMPIRICAL DISTRIBUTIONS--
   ANNALS OF MATH. STAT., 19, 1948.  177-189,
   (2) N. SMIRNOV--TABLE FOR ESTIMATING THE GOODNESS OF FIT
   OF EMPIRICAL DISTRIBUTIONS--ANNALS OF MATH. STAT., 19,
   1948.  279-281.
   (3) R. VON MISES--MATHEMATICAL THEORY OF PROBABILITY AND
   STATISTICS--ACADEMIC PRESS, NEW YORK, 1964.	490-493,
   (4) B.V. GNEDENKO--THE THEORY OF PROBABILITY--CHELSEA
   PUBLISHING COMPANY, NEW YORK, 1962.	384-401.