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- /* cdf/inverse_normal.c
- *
- * Copyright (C) 2002 Przemyslaw Sliwa and Jason H. Stover.
- *
- * This program is free software; you can redistribute it and/or modify
- * it under the terms of the GNU General Public License as published by
- * the Free Software Foundation; either version 3 of the License, or (at
- * your option) any later version.
- *
- * This program is distributed in the hope that it will be useful, but
- * WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
- * General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
- */
- /*
- * Computes the inverse normal cumulative distribution function
- * according to the algorithm shown in
- *
- * Wichura, M.J. (1988).
- * Algorithm AS 241: The Percentage Points of the Normal Distribution.
- * Applied Statistics, 37, 477-484.
- */
- #include "gsl__config.h"
- #include "gsl_errno.h"
- #include "gsl_math.h"
- #include "gsl_cdf.h"
- #include "gsl_cdf__rat_eval.h"
- static double
- small (double q)
- {
- const double a[8] = { 3.387132872796366608, 133.14166789178437745,
- 1971.5909503065514427, 13731.693765509461125,
- 45921.953931549871457, 67265.770927008700853,
- 33430.575583588128105, 2509.0809287301226727
- };
- const double b[8] = { 1.0, 42.313330701600911252,
- 687.1870074920579083, 5394.1960214247511077,
- 21213.794301586595867, 39307.89580009271061,
- 28729.085735721942674, 5226.495278852854561
- };
- double r = 0.180625 - q * q;
- double x = q * rat_eval (a, 8, b, 8, r);
- return x;
- }
- static double
- intermediate (double r)
- {
- const double a[] = { 1.42343711074968357734, 4.6303378461565452959,
- 5.7694972214606914055, 3.64784832476320460504,
- 1.27045825245236838258, 0.24178072517745061177,
- 0.0227238449892691845833, 7.7454501427834140764e-4
- };
- const double b[] = { 1.0, 2.05319162663775882187,
- 1.6763848301838038494, 0.68976733498510000455,
- 0.14810397642748007459, 0.0151986665636164571966,
- 5.475938084995344946e-4, 1.05075007164441684324e-9
- };
- double x = rat_eval (a, 8, b, 8, (r - 1.6));
- return x;
- }
- static double
- tail (double r)
- {
- const double a[] = { 6.6579046435011037772, 5.4637849111641143699,
- 1.7848265399172913358, 0.29656057182850489123,
- 0.026532189526576123093, 0.0012426609473880784386,
- 2.71155556874348757815e-5, 2.01033439929228813265e-7
- };
- const double b[] = { 1.0, 0.59983220655588793769,
- 0.13692988092273580531, 0.0148753612908506148525,
- 7.868691311456132591e-4, 1.8463183175100546818e-5,
- 1.4215117583164458887e-7, 2.04426310338993978564e-15
- };
- double x = rat_eval (a, 8, b, 8, (r - 5.0));
- return x;
- }
- double
- gsl_cdf_ugaussian_Pinv (const double P)
- {
- double r, x, pp;
- double dP = P - 0.5;
- if (P == 1.0)
- {
- return GSL_POSINF;
- }
- else if (P == 0.0)
- {
- return GSL_NEGINF;
- }
- if (fabs (dP) <= 0.425)
- {
- x = small (dP);
- return x;
- }
- pp = (P < 0.5) ? P : 1.0 - P;
- r = sqrt (-log (pp));
- if (r <= 5.0)
- {
- x = intermediate (r);
- }
- else
- {
- x = tail (r);
- }
- if (P < 0.5)
- {
- return -x;
- }
- else
- {
- return x;
- }
- }
- double
- gsl_cdf_ugaussian_Qinv (const double Q)
- {
- double r, x, pp;
- double dQ = Q - 0.5;
- if (Q == 1.0)
- {
- return GSL_NEGINF;
- }
- else if (Q == 0.0)
- {
- return GSL_POSINF;
- }
- if (fabs (dQ) <= 0.425)
- {
- x = small (dQ);
- return -x;
- }
- pp = (Q < 0.5) ? Q : 1.0 - Q;
- r = sqrt (-log (pp));
- if (r <= 5.0)
- {
- x = intermediate (r);
- }
- else
- {
- x = tail (r);
- }
- if (Q < 0.5)
- {
- return x;
- }
- else
- {
- return -x;
- }
- }
- double
- gsl_cdf_gaussian_Pinv (const double P, const double sigma)
- {
- return sigma * gsl_cdf_ugaussian_Pinv (P);
- }
- double
- gsl_cdf_gaussian_Qinv (const double Q, const double sigma)
- {
- return sigma * gsl_cdf_ugaussian_Qinv (Q);
- }
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