| /* 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 2 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 <config.h> |
| #include <gsl/gsl_errno.h> |
| #include <gsl/gsl_math.h> |
| #include <gsl/gsl_cdf.h> |
| |
| #include "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); |
| } |