diff options
Diffstat (limited to 'gsl-1.9/cdf/gaussinv.c')
-rw-r--r-- | gsl-1.9/cdf/gaussinv.c | 202 |
1 files changed, 202 insertions, 0 deletions
diff --git a/gsl-1.9/cdf/gaussinv.c b/gsl-1.9/cdf/gaussinv.c new file mode 100644 index 0000000..fbddb9e --- /dev/null +++ b/gsl-1.9/cdf/gaussinv.c @@ -0,0 +1,202 @@ +/* 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); +} |