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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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, 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 #include #include #include #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); }