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|
#include "v3p_netlib.h"
#undef abs
#undef min
#undef max
#include <math.h>
#include <stdio.h>
#define abs(x) ((x) >= 0 ? (x) : -(x))
#define min(a,b) ((a) <= (b) ? (a) : (b))
#define max(a,b) ((a) >= (b) ? (a) : (b))
extern double sqrt(double), exp(double), pow(double,double), log(double); /* #include <math.h> */
static void norcdf_(real *x, real *cdf);
static void dnorcdf_(doublereal *x, doublereal *cdf);
/* Subroutine */ void chscdf_(real *x, integer *nu, real *cdf)
{
/* Initialized data */
integer nucut = 1000;
doublereal b43 = 17.;
doublereal pi = 3.14159265358979;
doublereal dpower = .33333333333333;
doublereal b11 = .33333333333333;
doublereal b21 = -.02777777777778;
doublereal b31 = -6.1728395061e-4;
doublereal b32 = -13.;
doublereal b41 = 1.8004115226e-4;
doublereal b42 = 6.;
/* Local variables */
real cdfn;
integer imin, imax;
doublereal term, term0, term1, term2, term3, term4;
integer i;
doublereal dcdfn, dfact;
real amean, u, z;
integer ibran;
real spchi;
doublereal d1, d2, d3, ai;
real sd;
doublereal dw, dx;
integer ievodd;
doublereal chi;
real anu;
doublereal danu, danu2, dnu;
doublereal sum;
/* PURPOSE--THIS SUBROUTINE COMPUTES THE CUMULATIVE DISTRIBUTION */
/* FUNCTION VALUE FOR THE CHI-SQUARED DISTRIBUTION */
/* WITH INTEGER DEGREES OF FREEDOM PARAMETER = NU. */
/* THIS DISTRIBUTION IS DEFINED FOR ALL NON-NEGATIVE X. */
/* THE PROBABILITY DENSITY FUNCTION IS GIVEN */
/* IN THE REFERENCES BELOW. */
/* INPUT ARGUMENTS--X = THE SINGLE PRECISION VALUE AT */
/* WHICH THE CUMULATIVE DISTRIBUTION */
/* FUNCTION IS TO BE EVALUATED. */
/* X SHOULD BE NON-NEGATIVE. */
/* --NU = THE INTEGER NUMBER OF DEGREES */
/* OF FREEDOM. */
/* NU SHOULD BE POSITIVE. */
/* OUTPUT ARGUMENTS--CDF = THE SINGLE PRECISION CUMULATIVE */
/* DISTRIBUTION FUNCTION VALUE. */
/* OUTPUT--THE SINGLE PRECISION CUMULATIVE DISTRIBUTION */
/* FUNCTION VALUE CDF FOR THE CHI-SQUARED DISTRIBUTION */
/* WITH DEGREES OF FREEDOM PARAMETER = NU. */
/* PRINTING--NONE UNLESS AN INPUT ARGUMENT ERROR CONDITION EXISTS. */
/* RESTRICTIONS--X SHOULD BE NON-NEGATIVE. */
/* --NU SHOULD BE A POSITIVE INTEGER VARIABLE. */
/* OTHER DATAPAC SUBROUTINES NEEDED--NORCDF. */
/* FORTRAN LIBRARY SUBROUTINES NEEDED--DSQRT, DEXP. */
/* MODE OF INTERNAL OPERATIONS--DOUBLE PRECISION. */
/* LANGUAGE--ANSI FORTRAN. */
/* REFERENCES--NATIONAL BUREAU OF STANDARDS APPLIED MATHEMATICS */
/* SERIES 55, 1964, PAGE 941, FORMULAE 26.4.4 AND 26.4.5.*/
/* --JOHNSON AND KOTZ, CONTINUOUS UNIVARIATE */
/* DISTRIBUTIONS--1, 1970, PAGE 176, */
/* FORMULA 28, AND PAGE 180, FORMULA 33.1. */
/* --OWEN, HANDBOOK OF STATISTICAL TABLES, */
/* 1962, PAGES 50-55. */
/* --PEARSON AND HARTLEY, BIOMETRIKA TABLES */
/* FOR STATISTICIANS, VOLUME 1, 1954, */
/* PAGES 122-131. */
/* WRITTEN BY--JAMES J. FILLIBEN */
/* STATISTICAL ENGINEERING LABORATORY (205.03) */
/* NATIONAL BUREAU OF STANDARDS */
/* WASHINGTON, D. C. 20234 */
/* PHONE: 301-921-2315 */
/* ORIGINAL VERSION--JUNE 1972. */
/* UPDATED --MAY 1974. */
/* UPDATED --SEPTEMBER 1975. */
/* UPDATED --NOVEMBER 1975. */
/* UPDATED --OCTOBER 1976. */
/* */
/* --------------------------------------------------------------------- */
/* CHECK THE INPUT ARGUMENTS FOR ERRORS */
if (*nu <= 0) {
fprintf(stderr,"(***** FATAL ERROR--THE SECOND INPUT ARGUMENT TO THE CHSCDF SUBROUTINE IS NON-POSITIVE *****)");
fprintf(stderr,"(***** THE VALUE OF THE ARGUMENT IS %ld *****\002)",*nu);
*cdf = 0.f;
return;
}
if (*x < 0.f) {
fprintf(stderr,"(***** NON-FATAL DIAGNOSTIC--THE FIRST INPUT ARGUMENT TO THE CHSCDF SUBROUTINE IS NEGATIVE *****)");
fprintf(stderr,"(***** THE VALUE OF THE ARGUMENT IS %f *****\002)",*x);
*cdf = 0.f;
return;
}
dx = *x;
anu = (real) (*nu);
dnu = (doublereal) (*nu);
/* IF X IS NON-POSITIVE, SET CDF = 0.0 AND RETURN. */
/* IF NU IS SMALLER THAN 10 AND X IS MORE THAN 200 */
/* STANDARD DEVIATIONS BELOW THE MEAN, */
/* SET CDF = 0.0 AND RETURN. */
/* IF NU IS 10 OR LARGER AND X IS MORE THAN 100 */
/* STANDARD DEVIATIONS BELOW THE MEAN, */
/* SET CDF = 0.0 AND RETURN. */
/* IF NU IS SMALLER THAN 10 AND X IS MORE THAN 200 */
/* STANDARD DEVIATIONS ABOVE THE MEAN, */
/* SET CDF = 1.0 AND RETURN. */
/* IF NU IS 10 OR LARGER AND X IS MORE THAN 100 */
/* STANDARD DEVIATIONS ABOVE THE MEAN, */
/* SET CDF = 1.0 AND RETURN. */
if (*x <= 0.f) {
*cdf = 0.f;
return;
}
amean = anu;
sd = (float)sqrt(anu * 2.f);
z = (*x - amean) / sd;
if (*nu < 10 && z < -200.f) {
*cdf = 0.f;
return;
}
if (*nu >= 10 && z < -100.f) {
*cdf = 0.f;
return;
}
if (*nu < 10 && z > 200.f) {
*cdf = 1.f;
return;
}
if (*nu >= 10 && z > 100.f) {
*cdf = 1.f;
return;
}
/* DISTINGUISH BETWEEN 3 SEPARATE REGIONS */
/* OF THE (X,NU) SPACE. */
/* BRANCH TO THE PROPER COMPUTATIONAL METHOD */
/* DEPENDING ON THE REGION. */
/* NUCUT HAS THE VALUE 1000. */
if (*nu < nucut) {
goto L1000;
}
if (*nu >= nucut && *x <= anu) {
goto L2000;
}
if (*nu >= nucut && *x > anu) {
goto L3000;
}
ibran = 1;
fprintf(stderr,"(*****INTERNAL ERROR IN CHSCDF SUBROUTINE -- IMPOSSIBLE BRANCH CONDITION AT BRANCH POINT %ld)",ibran);
return;
/* TREAT THE SMALL AND MODERATE DEGREES OF FREEDOM CASE */
/* (THAT IS, WHEN NU IS SMALLER THAN 1000). */
/* METHOD UTILIZED--EXACT FINITE SUM */
/* (SEE AMS 55, PAGE 941, FORMULAE 26.4.4 AND 26.4.5). */
L1000:
chi = sqrt(dx);
ievodd = *nu - (*nu / 2 << 1);
if (ievodd == 0) {
sum = 1.;
term = 1.;
imin = 2;
imax = *nu - 2;
}
else {
sum = 0.;
term = 1.f / chi;
imin = 1;
imax = *nu - 1;
}
if (imin <= imax)
for (i = imin; i <= imax; i += 2) {
ai = (doublereal) i;
term *= dx / ai;
sum += term;
}
sum *= exp(-dx / 2.);
if (ievodd != 0) {
sum *= sqrt(2. / pi);
spchi = (float)chi;
norcdf_(&spchi, &cdfn);
dcdfn = cdfn;
sum += (1. - dcdfn) * 2.;
}
*cdf = 1.f - (float)sum;
return;
/* TREAT THE CASE WHEN NU IS LARGE */
/* (THAT IS, WHEN NU IS EQUAL TO OR GREATER THAN 1000) */
/* AND X IS LESS THAN OR EQUAL TO NU. */
/* METHOD UTILIZED--WILSON-HILFERTY APPROXIMATION */
/* (SEE JOHNSON AND KOTZ, VOLUME 1, PAGE 176, FORMULA 28). */
L2000:
dfact = dnu * 4.5;
u = (float)(dx / dnu);
u = (float)((pow(u, dpower) - 1.0 + 1.0 / dfact) * sqrt(dfact));
norcdf_(&u, &cdfn);
*cdf = cdfn;
return;
/* TREAT THE CASE WHEN NU IS LARGE */
/* (THAT IS, WHEN NU IS EQUAL TO OR GREATER THAN 1000) */
/* AND X IS LARGER THAN NU. */
/* METHOD UTILIZED--HILL'S ASYMPTOTIC EXPANSION */
/* (SEE JOHNSON AND KOTZ, VOLUME 1, PAGE 180, FORMULA 33.1). */
L3000:
dw = sqrt(dx - dnu - dnu * log(dx / dnu));
danu = sqrt(2.0 / dnu);
d1 = dw;
d2 = dw * dw;
d3 = dw * d2;
term0 = dw;
term1 = b11 * danu;
danu2 = danu * danu;
term2 = b21 * d1 * danu2;
term3 = b31 * (d2 + b32) * danu * danu2;
term4 = b41 * (b42 * d3 + b43 * d1) * danu2 * danu2;
u = (float)(term0 + term1 + term2 + term3 + term4);
norcdf_(&u, &cdfn);
*cdf = cdfn;
} /* chscdf_ */
/* Subroutine */
static void norcdf_(real *x, real *cdf)
{
/* Initialized data */
real b1 = .31938153f;
real b2 = -.356563782f;
real b3 = 1.781477937f;
real b4 = -1.821255978f;
real b5 = 1.330274429f;
real p = .2316419f;
/* System generated locals */
real tt;
/* Local variables */
real t, z;
/* PURPOSE--THIS SUBROUTINE COMPUTES THE CUMULATIVE DISTRIBUTION */
/* FUNCTION VALUE FOR THE NORMAL (GAUSSIAN) */
/* DISTRIBUTION WITH MEAN = 0 AND STANDARD DEVIATION = 1. */
/* THIS DISTRIBUTION IS DEFINED FOR ALL X AND HAS */
/* THE PROBABILITY DENSITY FUNCTION */
/* F(X) = (1/SQRT(2*PI))*EXP(-X*X/2). */
/* INPUT ARGUMENTS--X = THE SINGLE PRECISION VALUE AT */
/* WHICH THE CUMULATIVE DISTRIBUTION */
/* FUNCTION IS TO BE EVALUATED. */
/* OUTPUT ARGUMENTS--CDF = THE SINGLE PRECISION CUMULATIVE */
/* DISTRIBUTION FUNCTION VALUE. */
/* OUTPUT--THE SINGLE PRECISION CUMULATIVE DISTRIBUTION */
/* FUNCTION VALUE CDF. */
/* PRINTING--NONE. */
/* RESTRICTIONS--NONE. */
/* OTHER DATAPAC SUBROUTINES NEEDED--NONE. */
/* FORTRAN LIBRARY SUBROUTINES NEEDED--EXP. */
/* MODE OF INTERNAL OPERATIONS--SINGLE PRECISION. */
/* LANGUAGE--ANSI FORTRAN. */
/* REFERENCES--NATIONAL BUREAU OF STANDARDS APPLIED MATHEMATICS */
/* SERIES 55, 1964, PAGE 932, FORMULA 26.2.17. */
/* --JOHNSON AND KOTZ, CONTINUOUS UNIVARIATE */
/* DISTRIBUTIONS--1, 1970, PAGES 40-111. */
/* WRITTEN BY--JAMES J. FILLIBEN */
/* STATISTICAL ENGINEERING LABORATORY (205.03) */
/* NATIONAL BUREAU OF STANDARDS */
/* WASHINGTON, D. C. 20234 */
/* PHONE: 301-921-2315 */
/* ORIGINAL VERSION--JUNE 1972. */
/* UPDATED --SEPTEMBER 1975. */
/* UPDATED --NOVEMBER 1975. */
/* */
/* --------------------------------------------------------------------- */
/* CHECK THE INPUT ARGUMENTS FOR ERRORS. */
/* NO INPUT ARGUMENT ERRORS POSSIBLE FOR THIS DISTRIBUTION. */
z = *x;
if (z < 0.f)
z = -z;
t = 1.f / (p * z + 1.f);
tt = t*t;
*cdf = 1.f - (float)exp(z * -.5f * z) * .39894228040143f * (b1 * t + b2 * tt + b3 * t*tt + b4 * tt*tt + b5 * t*tt*tt);
if (*x < 0.f) {
*cdf = 1.f - *cdf;
}
} /* norcdf_ */
/* Subroutine */ void dchscdf_(doublereal* x, integer* nu, doublereal* cdf)
{
/* Initialized data */
integer nucut = 1000;
doublereal b43 = 17.;
doublereal pi = 3.14159265358979;
doublereal dpower = .333333333333333333;
doublereal b11 = .333333333333333333;
doublereal b21 = -.027777777777777778;
doublereal b31 = -6.1728395061e-4;
doublereal b32 = -13.;
doublereal b41 = 1.8004115226e-4;
doublereal b42 = 6.;
/* System generated locals */
doublereal danu2;
/* Local variables */
doublereal cdfn, danu;
integer imin, imax;
doublereal term, term0, term1, term2, term3, term4;
integer i;
doublereal dcdfn, dfact;
doublereal amean, u, z;
integer ibran;
doublereal spchi;
doublereal d1, d2, d3, ai;
doublereal sd;
doublereal dw, dx;
integer ievodd;
doublereal chi;
doublereal anu;
doublereal dnu;
doublereal sum;
/* PURPOSE--THIS SUBROUTINE COMPUTES THE CUMULATIVE DISTRIBUTION */
/* FUNCTION VALUE FOR THE CHI-SQUARED DISTRIBUTION */
/* WITH INTEGER DEGREES OF FREEDOM PARAMETER = NU. */
/* THIS DISTRIBUTION IS DEFINED FOR ALL NON-NEGATIVE X. */
/* THE PROBABILITY DENSITY FUNCTION IS GIVEN */
/* IN THE REFERENCES BELOW. */
/* INPUT ARGUMENTS--X = THE DOUBLE PRECISION VALUE AT */
/* WHICH THE CUMULATIVE DISTRIBUTION */
/* FUNCTION IS TO BE EVALUATED. */
/* X SHOULD BE NON-NEGATIVE. */
/* --NU = THE INTEGER NUMBER OF DEGREES */
/* OF FREEDOM. */
/* NU SHOULD BE POSITIVE. */
/* OUTPUT ARGUMENTS--CDF = THE DOUBLE PRECISION CUMULATIVE */
/* DISTRIBUTION FUNCTION VALUE. */
/* OUTPUT--THE DOUBLE PRECISION CUMULATIVE DISTRIBUTION */
/* FUNCTION VALUE CDF FOR THE CHI-SQUARED DISTRIBUTION */
/* WITH DEGREES OF FREEDOM PARAMETER = NU. */
/* PRINTING--NONE UNLESS AN INPUT ARGUMENT ERROR CONDITION EXISTS. */
/* RESTRICTIONS--X SHOULD BE NON-NEGATIVE. */
/* --NU SHOULD BE A POSITIVE INTEGER VARIABLE. */
/* OTHER DATAPAC SUBROUTINES NEEDED--NORCDF. */
/* FORTRAN LIBRARY SUBROUTINES NEEDED--DSQRT, DEXP. */
/* MODE OF INTERNAL OPERATIONS--DOUBLE PRECISION. */
/* LANGUAGE--ANSI FORTRAN. */
/* REFERENCES--NATIONAL BUREAU OF STANDARDS APPLIED MATHEMATICS */
/* SERIES 55, 1964, PAGE 941, FORMULAE 26.4.4 AND 26.4.5.*/
/* --JOHNSON AND KOTZ, CONTINUOUS UNIVARIATE */
/* DISTRIBUTIONS--1, 1970, PAGE 176, */
/* FORMULA 28, AND PAGE 180, FORMULA 33.1. */
/* --OWEN, HANDBOOK OF STATISTICAL TABLES, */
/* 1962, PAGES 50-55. */
/* --PEARSON AND HARTLEY, BIOMETRIKA TABLES */
/* FOR STATISTICIANS, VOLUME 1, 1954, */
/* PAGES 122-131. */
/* WRITTEN BY--JAMES J. FILLIBEN */
/* STATISTICAL ENGINEERING LABORATORY (205.03) */
/* NATIONAL BUREAU OF STANDARDS */
/* WASHINGTON, D. C. 20234 */
/* PHONE: 301-921-2315 */
/* ORIGINAL VERSION--JUNE 1972. */
/* UPDATED --MAY 1974. */
/* UPDATED --SEPTEMBER 1975. */
/* UPDATED --NOVEMBER 1975. */
/* UPDATED --OCTOBER 1976. */
/* */
/* --------------------------------------------------------------------- */
/* CHECK THE INPUT ARGUMENTS FOR ERRORS */
if (*nu <= 0) {
fprintf(stderr,"(***** FATAL ERROR--THE SECOND INPUT ARGUMENT TO THE CHSCDF SUBROUTINE IS NON-POSITIVE *****)");
fprintf(stderr,"(***** THE VALUE OF THE ARGUMENT IS %ld *****\002)",*nu);
*cdf = 0.0;
return;
}
if (*x < 0.0) {
fprintf(stderr,"(***** NON-FATAL DIAGNOSTIC--THE FIRST INPUT ARGUMENT TO THE CHSCDF SUBROUTINE IS NEGATIVE *****)");
fprintf(stderr,"(***** THE VALUE OF THE ARGUMENT IS %f *****\002)",*x);
*cdf = 0.0;
return;
}
dx = *x;
anu = (doublereal) (*nu);
dnu = (doublereal) (*nu);
/* IF X IS NON-POSITIVE, SET CDF = 0.0 AND RETURN. */
/* IF NU IS SMALLER THAN 10 AND X IS MORE THAN 200 */
/* STANDARD DEVIATIONS BELOW THE MEAN, */
/* SET CDF = 0.0 AND RETURN. */
/* IF NU IS 10 OR LARGER AND X IS MORE THAN 100 */
/* STANDARD DEVIATIONS BELOW THE MEAN, */
/* SET CDF = 0.0 AND RETURN. */
/* IF NU IS SMALLER THAN 10 AND X IS MORE THAN 200 */
/* STANDARD DEVIATIONS ABOVE THE MEAN, */
/* SET CDF = 1.0 AND RETURN. */
/* IF NU IS 10 OR LARGER AND X IS MORE THAN 100 */
/* STANDARD DEVIATIONS ABOVE THE MEAN, */
/* SET CDF = 1.0 AND RETURN. */
if (*x <= 0.0) {
*cdf = 0.0;
return;
}
amean = anu;
sd = sqrt(anu * 2.0);
z = (*x - amean) / sd;
if (*nu < 10 && z < -200.0) {
*cdf = 0.0;
return;
}
if (*nu >= 10 && z < -100.0) {
*cdf = 0.0;
return;
}
if (*nu < 10 && z > 200.0) {
*cdf = 1.0;
return;
}
if (*nu >= 10 && z > 100.0) {
*cdf = 1.0;
return;
}
/* DISTINGUISH BETWEEN 3 SEPARATE REGIONS */
/* OF THE (X,NU) SPACE. */
/* BRANCH TO THE PROPER COMPUTATIONAL METHOD */
/* DEPENDING ON THE REGION. */
/* NUCUT HAS THE VALUE 1000. */
if (*nu < nucut) {
goto L1000;
}
if (*nu >= nucut && *x <= anu) {
goto L2000;
}
if (*nu >= nucut && *x > anu) {
goto L3000;
}
ibran = 1;
fprintf(stderr,"(*****INTERNAL ERROR IN CHSCDF SUBROUTINE -- IMPOSSIBLE BRANCH CONDITION AT BRANCH POINT %ld)",ibran);
return;
/* TREAT THE SMALL AND MODERATE DEGREES OF FREEDOM CASE */
/* (THAT IS, WHEN NU IS SMALLER THAN 1000). */
/* METHOD UTILIZED--EXACT FINITE SUM */
/* (SEE AMS 55, PAGE 941, FORMULAE 26.4.4 AND 26.4.5). */
L1000:
chi = sqrt(dx);
ievodd = *nu - (*nu / 2 << 1);
if (ievodd == 0) {
sum = 1.;
term = 1.;
imin = 2;
imax = *nu - 2;
}
else {
sum = 0.;
term = 1.0 / chi;
imin = 1;
imax = *nu - 1;
}
if (imin <= imax)
for (i = imin; i <= imax; i += 2) {
ai = (doublereal) i;
term *= dx / ai;
sum += term;
}
sum *= exp(-dx / 2.);
if (ievodd != 0) {
sum *= sqrt(2. / pi);
spchi = chi;
dnorcdf_(&spchi, &cdfn);
dcdfn = cdfn;
sum += (1. - dcdfn) * 2.;
}
*cdf = 1.0 - sum;
if (*cdf < 0.0) *cdf = 0.0;
return;
/* TREAT THE CASE WHEN NU IS LARGE */
/* (THAT IS, WHEN NU IS EQUAL TO OR GREATER THAN 1000) */
/* AND X IS LESS THAN OR EQUAL TO NU. */
/* METHOD UTILIZED--WILSON-HILFERTY APPROXIMATION */
/* (SEE JOHNSON AND KOTZ, VOLUME 1, PAGE 176, FORMULA 28). */
L2000:
dfact = dnu * 4.5;
u = dx / dnu;
u = (pow(u, dpower) - 1.0 + 1.0 / dfact) * sqrt(dfact);
dnorcdf_(&u, &cdfn);
*cdf = cdfn;
return;
/* TREAT THE CASE WHEN NU IS LARGE */
/* (THAT IS, WHEN NU IS EQUAL TO OR GREATER THAN 1000) */
/* AND X IS LARGER THAN NU. */
/* METHOD UTILIZED--HILL'S ASYMPTOTIC EXPANSION */
/* (SEE JOHNSON AND KOTZ, VOLUME 1, PAGE 180, FORMULA 33.1). */
L3000:
dw = sqrt(dx - dnu - dnu * log(dx / dnu));
danu = sqrt(2.0 / dnu);
d1 = dw;
d2 = dw * dw;
d3 = dw * d2;
term0 = dw;
term1 = b11 * danu;
danu2 = danu * danu;
term2 = b21 * d1 * danu2;
term3 = b31 * (d2 + b32) * danu * danu2;
term4 = b41 * (b42 * d3 + b43 * d1) * danu2 * danu2;
u = term0 + term1 + term2 + term3 + term4;
dnorcdf_(&u, &cdfn);
*cdf = cdfn;
} /* dchscdf_ */
/* Subroutine */
static void dnorcdf_(doublereal* x, doublereal* cdf)
{
/* Initialized data */
doublereal b1 = .31938153;
doublereal b2 = -.356563782;
doublereal b3 = 1.781477937;
doublereal b4 = -1.821255978;
doublereal b5 = 1.330274429;
doublereal p = .2316419;
/* System generated locals */
doublereal tt;
/* Local variables */
doublereal t, z;
/* PURPOSE--THIS SUBROUTINE COMPUTES THE CUMULATIVE DISTRIBUTION */
/* FUNCTION VALUE FOR THE NORMAL (GAUSSIAN) */
/* DISTRIBUTION WITH MEAN = 0 AND STANDARD DEVIATION = 1. */
/* THIS DISTRIBUTION IS DEFINED FOR ALL X AND HAS */
/* THE PROBABILITY DENSITY FUNCTION */
/* F(X) = (1/SQRT(2*PI))*EXP(-X*X/2). */
/* INPUT ARGUMENTS--X = THE DOUBLE PRECISION VALUE AT */
/* WHICH THE CUMULATIVE DISTRIBUTION */
/* FUNCTION IS TO BE EVALUATED. */
/* OUTPUT ARGUMENTS--CDF = THE DOUBLE PRECISION CUMULATIVE */
/* DISTRIBUTION FUNCTION VALUE. */
/* OUTPUT--THE DOUBLE PRECISION CUMULATIVE DISTRIBUTION */
/* FUNCTION VALUE CDF. */
/* PRINTING--NONE. */
/* RESTRICTIONS--NONE. */
/* OTHER DATAPAC SUBROUTINES NEEDED--NONE. */
/* FORTRAN LIBRARY SUBROUTINES NEEDED--EXP. */
/* MODE OF INTERNAL OPERATIONS--DOUBLE PRECISION. */
/* LANGUAGE--ANSI FORTRAN. */
/* REFERENCES--NATIONAL BUREAU OF STANDARDS APPLIED MATHEMATICS */
/* SERIES 55, 1964, PAGE 932, FORMULA 26.2.17. */
/* --JOHNSON AND KOTZ, CONTINUOUS UNIVARIATE */
/* DISTRIBUTIONS--1, 1970, PAGES 40-111. */
/* WRITTEN BY--JAMES J. FILLIBEN */
/* STATISTICAL ENGINEERING LABORATORY (205.03) */
/* NATIONAL BUREAU OF STANDARDS */
/* WASHINGTON, D. C. 20234 */
/* PHONE: 301-921-2315 */
/* ORIGINAL VERSION--JUNE 1972. */
/* UPDATED --SEPTEMBER 1975. */
/* UPDATED --NOVEMBER 1975. */
/* */
/* --------------------------------------------------------------------- */
/* CHECK THE INPUT ARGUMENTS FOR ERRORS. */
/* NO INPUT ARGUMENT ERRORS POSSIBLE FOR THIS DISTRIBUTION. */
z = *x;
if (z < 0.0)
z = -z;
t = 1.0 / (p * z + 1.0);
tt = t*t;
*cdf = 1.0 - exp(z * -.5 * z) * .39894228040143 * (b1 * t + b2 * tt + b3 * t*tt + b4 * tt*tt + b5 * t*tt*tt);
if (*x < 0.0)
*cdf = 1.0 - *cdf;
if (*cdf < 0.0)
*cdf = 0.0;
} /* dnorcdf_ */
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