What are the Parameters for Algorithm AS 62 APPL. STATIST. (1973) VOL.22, NO.2
From: Roland (roland_at_nospam)
Date: 09/10/04
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Date: Fri, 10 Sep 2004 04:26:58 +0200
Does anyone know what the parameters mean in this one? I do not have access
to the original article.
Specifically, how do I interpret the FRQNCY array (how is it indexed)? TIA.
Here is the Fortran algorithm (http://lib.stat.cmu.edu/apstat/62):
c AS 62 generates the frequencies for the Mann-Whitney U-statistic.
c Users are much more likely to need the distribution function.
c Code to return the distribution function has been added at the end
c of AS 62 by Alan Miller. Remove the C's in column 1 to activate it.
c
SUBROUTINE UDIST(M, N, FRQNCY, LFR, WORK, LWRK, IFAULT)
C
C ALGORITHM AS 62 APPL. STATIST. (1973) VOL.22, NO.2
C
C The distribution of the Mann-Whitney U-statistic is generated for
C the two given sample sizes
C
INTEGER M, N, LFR, LWRK, IFAULT
REAL FRQNCY(LFR), WORK(LWRK)
C
C Local variables
C
INTEGER MINMN, MN1, MAXMN, N1, I, IN, L, K, J
REAL ZERO, ONE, SUM
DATA ZERO /0.0/, ONE /1.0/
C
C Check smaller sample size
C
IFAULT = 1
MINMN = MIN(M, N)
IF (MINMN .LT. 1) RETURN
C
C Check size of results array
C
IFAULT = 2
MN1 = M * N + 1
IF (LFR .LT. MN1) RETURN
C
C Set up results for 1st cycle and return if MINMN = 1
C
MAXMN = MAX(M, N)
N1 = MAXMN + 1
DO 1 I = 1, N1
1 FRQNCY(I) = ONE
IF (MINMN .EQ. 1) GO TO 4
C
C Check length of work array
C
IFAULT = 3
IF (LWRK .LT. (MN1 + 1) / 2 + MINMN) RETURN
C
C Clear rest of FREQNCY
C
N1 = N1 + 1
DO 2 I = N1, MN1
2 FRQNCY(I) = ZERO
C
C Generate successively higher order distributions
C
WORK(1) = ZERO
IN = MAXMN
DO 3 I = 2, MINMN
WORK(I) = ZERO
IN = IN + MAXMN
N1 = IN + 2
L = 1 + IN / 2
K = I
C
C Generate complete distribution from outside inwards
C
DO 3 J = 1, L
K = K + 1
N1 = N1 - 1
SUM = FRQNCY(J) + WORK(J)
FRQNCY(J) = SUM
WORK(K) = SUM - FRQNCY(N1)
FRQNCY(N1) = SUM
3 CONTINUE
C
4 IFAULT = 0
C
C Code to overwrite the frequency function with the distribution
C function. N.B. The frequency in FRQNCY(1) is for U = 0, and
C that in FRQNCY(I) is for U = I - 1.
C
C SUM = ZERO
C DO 10 I = 1, MN1
C SUM = SUM + FRQNCY(I)
C FRQNCY(I) = SUM
C 10 CONTINUE
C DO 20 I = 1, MN1
C 20 FRQNCY(I) = FRQNCY(I) / SUM
C
RETURN
END
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