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SUBROUTINE cumtnc(t,df,pnonc,cum,ccum)
C**********************************************************************
C
C SUBROUTINE CUMTNC(T,DF,PNONC,CUM,CCUM)
C
C CUMulative Non-Central T-distribution
C
C
C Function
C
C
C Computes the integral from -infinity to T of the non-central
C t-density.
C
C
C Arguments
C
C
C T --> Upper limit of integration of the non-central t-density.
C T is DOUBLE PRECISION
C
C DF --> Degrees of freedom of the non-central t-distribution.
C DF is DOUBLE PRECISIO
C
C PNONC --> Non-centrality parameter of the non-central t distibutio
C PNONC is DOUBLE PRECI
C
C CUM <-- Cumulative t-distribution.
C CCUM is DOUBLE PRECIS
C
C CCUM <-- Compliment of Cumulative t-distribution.
C CCUM is DOUBLE PRECIS
C
C
C Method
C
C Upper tail of the cumulative noncentral t using
C formulae from page 532 of Johnson, Kotz, Balakrishnan, Coninuous
C Univariate Distributions, Vol 2, 2nd Edition. Wiley (1995)
C
C This implementation starts the calculation at i = lambda,
C which is near the largest Di. It then sums forward and backward.
C***********************************************************************
C .. Parameters ..
DOUBLE PRECISION one,zero,half,two,onep5
PARAMETER (one=1.0d0,zero=0.0d0,half=0.5d0,two=2.0d0,onep5=1.5d0)
DOUBLE PRECISION conv
PARAMETER (conv=1.0d-7)
DOUBLE PRECISION tiny
PARAMETER (tiny=1.0d-10)
C ..
C .. Scalar Arguments ..
DOUBLE PRECISION ccum,cum,df,pnonc,t
C ..
C .. Local Scalars ..
DOUBLE PRECISION alghdf,b,bb,bbcent,bcent,cent,d,dcent,dpnonc,
+ dum1,dum2,e,ecent,halfdf,lambda,lnomx,lnx,omx,
+ pnonc2,s,scent,ss,sscent,t2,term,tt,twoi,x,
+ xi,xlnd,xlne
INTEGER ierr
LOGICAL qrevs
C ..
C .. External Functions ..
DOUBLE PRECISION gamln
EXTERNAL gamln
C ..
C .. External Subroutines ..
EXTERNAL bratio,cumnor,cumt
C ..
C .. Intrinsic Functions ..
INTRINSIC abs,exp,aint,log,max,min
C ..
C Case pnonc essentially zero
IF (abs(pnonc).LE.tiny) THEN
CALL cumt(t,df,cum,ccum)
RETURN
END IF
qrevs = t .LT. zero
IF (qrevs) THEN
tt = -t
dpnonc = -pnonc
ELSE
tt = t
dpnonc = pnonc
END IF
pnonc2 = dpnonc*dpnonc
t2 = tt*tt
IF (abs(tt).LE.tiny) THEN
CALL cumnor(-pnonc,cum,ccum)
RETURN
END IF
lambda = half*pnonc2
x = df/ (df+t2)
omx = one - x
lnx = log(x)
lnomx = log(omx)
halfdf = half*df
alghdf = gamln(halfdf)
C ******************** Case i = lambda
cent = aint(lambda)
IF (cent.LT.one) cent = one
C Compute d=T(2i) in log space and offset by exp(-lambda)
xlnd = cent*log(lambda) - gamln(cent+one) - lambda
dcent = exp(xlnd)
C Compute e=t(2i+1) in log space offset by exp(-lambda)
xlne = (cent+half)*log(lambda) - gamln(cent+onep5) - lambda
ecent = exp(xlne)
IF (dpnonc.LT.zero) ecent = -ecent
C Compute bcent=B(2*cent)
CALL bratio(halfdf,cent+half,x,omx,bcent,dum1,ierr)
C compute bbcent=B(2*cent+1)
CALL bratio(halfdf,cent+one,x,omx,bbcent,dum2,ierr)
C Case bcent and bbcent are essentially zero
C Thus t is effectively infinite
IF ((bcent+bbcent).LT.tiny) THEN
IF (qrevs) THEN
cum = zero
ccum = one
ELSE
cum = one
ccum = zero
END IF
RETURN
END IF
C Case bcent and bbcent are essentially one
C Thus t is effectively zero
IF ((dum1+dum2).LT.tiny) THEN
CALL cumnor(-pnonc,cum,ccum)
RETURN
END IF
C First term in ccum is D*B + E*BB
ccum = dcent*bcent + ecent*bbcent
C compute s(cent) = B(2*(cent+1)) - B(2*cent))
scent = gamln(halfdf+cent+half) - gamln(cent+onep5) - alghdf +
+ halfdf*lnx + (cent+half)*lnomx
scent = exp(scent)
C compute ss(cent) = B(2*cent+3) - B(2*cent+1)
sscent = gamln(halfdf+cent+one) - gamln(cent+two) - alghdf +
+ halfdf*lnx + (cent+one)*lnomx
sscent = exp(sscent)
C ******************** Sum Forward
xi = cent + one
twoi = two*xi
d = dcent
e = ecent
b = bcent
bb = bbcent
s = scent
ss = sscent
10 b = b + s
bb = bb + ss
d = (lambda/xi)*d
e = (lambda/ (xi+half))*e
term = d*b + e*bb
ccum = ccum + term
s = s*omx* (df+twoi-one)/ (twoi+one)
ss = ss*omx* (df+twoi)/ (twoi+two)
xi = xi + one
twoi = two*xi
IF (abs(term).GT.conv*ccum) GO TO 10
C ******************** Sum Backward
xi = cent
twoi = two*xi
d = dcent
e = ecent
b = bcent
bb = bbcent
s = scent* (one+twoi)/ ((df+twoi-one)*omx)
ss = sscent* (two+twoi)/ ((df+twoi)*omx)
20 b = b - s
bb = bb - ss
d = d* (xi/lambda)
e = e* ((xi+half)/lambda)
term = d*b + e*bb
ccum = ccum + term
xi = xi - one
IF (xi.LT.half) GO TO 30
twoi = two*xi
s = s* (one+twoi)/ ((df+twoi-one)*omx)
ss = ss* (two+twoi)/ ((df+twoi)*omx)
IF (abs(term).GT.conv*ccum) GO TO 20
30 CONTINUE
IF (qrevs) THEN
cum = half*ccum
ccum = one - cum
ELSE
ccum = half*ccum
cum = one - ccum
END IF
C Due to roundoff error the answer may not lie between zero and one
C Force it to do so
cum = max(min(cum,one),zero)
ccum = max(min(ccum,one),zero)
RETURN
END
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