diff options
Diffstat (limited to 'gsl-1.9/cdf/tdistinv.c')
| -rw-r--r-- | gsl-1.9/cdf/tdistinv.c | 232 |
1 files changed, 232 insertions, 0 deletions
diff --git a/gsl-1.9/cdf/tdistinv.c b/gsl-1.9/cdf/tdistinv.c new file mode 100644 index 0000000..63ac409 --- /dev/null +++ b/gsl-1.9/cdf/tdistinv.c @@ -0,0 +1,232 @@ +/* cdf/tdistinv.c + * + * Copyright (C) 2002 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. + */ + +#include <config.h> +#include <math.h> +#include <gsl/gsl_cdf.h> +#include <gsl/gsl_math.h> +#include <gsl/gsl_randist.h> +#include <gsl/gsl_sf_gamma.h> + +#include <stdio.h> + +static double +inv_cornish_fisher (double z, double nu) +{ + double a = 1 / (nu - 0.5); + double b = 48.0 / (a * a); + + double cf1 = z * (3 + z * z); + double cf2 = z * (945 + z * z * (360 + z * z * (63 + z * z * 4))); + + double y = z - cf1 / b + cf2 / (10 * b * b); + + double t = GSL_SIGN (z) * sqrt (nu * expm1 (a * y * y)); + + return t; +} + + +double +gsl_cdf_tdist_Pinv (const double P, const double nu) +{ + double x, ptail; + + if (P == 1.0) + { + return GSL_POSINF; + } + else if (P == 0.0) + { + return GSL_NEGINF; + } + + if (nu == 1.0) + { + x = tan (M_PI * (P - 0.5)); + } + else if (nu == 2.0) + { + double a = 2 * P - 1; + x = a / sqrt (2 * (1 - a * a)); + } + + ptail = (P < 0.5) ? P : 1 - P; + + if (sqrt (M_PI * nu / 2) * ptail > pow (0.05, nu / 2)) + { + double xg = gsl_cdf_ugaussian_Pinv (P); + x = inv_cornish_fisher (xg, nu); + } + else + { + /* Use an asymptotic expansion of the tail of integral */ + + double beta = gsl_sf_beta (0.5, nu / 2); + + if (P < 0.5) + { + x = -sqrt (nu) * pow (beta * nu * P, -1.0 / nu); + } + else + { + x = sqrt (nu) * pow (beta * nu * (1 - P), -1.0 / nu); + } + + /* Correct nu -> nu/(1+nu/x^2) in the leading term to account + for higher order terms. This avoids overestimating x, which + makes the iteration unstable due to the rapidly decreasing + tails of the distribution. */ + + x /= sqrt (1 + nu / (x * x)); + } + + { + double dP, phi; + unsigned int n = 0; + + start: + dP = P - gsl_cdf_tdist_P (x, nu); + phi = gsl_ran_tdist_pdf (x, nu); + + if (dP == 0.0 || n++ > 32) + goto end; + + { + double lambda = dP / phi; + double step0 = lambda; + double step1 = ((nu + 1) * x / (x * x + nu)) * (lambda * lambda / 4.0); + + double step = step0; + + if (fabs (step1) < fabs (step0)) + { + step += step1; + } + + if (P > 0.5 && x + step < 0) + x /= 2; + else if (P < 0.5 && x + step > 0) + x /= 2; + else + x += step; + + if (fabs (step) > 1e-10 * fabs (x)) + goto start; + } + } + +end: + + return x; +} + +double +gsl_cdf_tdist_Qinv (const double Q, const double nu) +{ + double x, qtail; + + if (Q == 0.0) + { + return GSL_POSINF; + } + else if (Q == 1.0) + { + return GSL_NEGINF; + } + + if (nu == 1.0) + { + x = tan (M_PI * (0.5 - Q)); + } + else if (nu == 2.0) + { + double a = 2 * (1 - Q) - 1; + x = a / sqrt (2 * (1 - a * a)); + } + + qtail = (Q < 0.5) ? Q : 1 - Q; + + if (sqrt (M_PI * nu / 2) * qtail > pow (0.05, nu / 2)) + { + double xg = gsl_cdf_ugaussian_Qinv (Q); + x = inv_cornish_fisher (xg, nu); + } + else + { + /* Use an asymptotic expansion of the tail of integral */ + + double beta = gsl_sf_beta (0.5, nu / 2); + + if (Q < 0.5) + { + x = sqrt (nu) * pow (beta * nu * Q, -1.0 / nu); + } + else + { + x = -sqrt (nu) * pow (beta * nu * (1 - Q), -1.0 / nu); + } + + /* Correct nu -> nu/(1+nu/x^2) in the leading term to account + for higher order terms. This avoids overestimating x, which + makes the iteration unstable due to the rapidly decreasing + tails of the distribution. */ + + x /= sqrt (1 + nu / (x * x)); + } + + { + double dQ, phi; + unsigned int n = 0; + + start: + dQ = Q - gsl_cdf_tdist_Q (x, nu); + phi = gsl_ran_tdist_pdf (x, nu); + + if (dQ == 0.0 || n++ > 32) + goto end; + + { + double lambda = - dQ / phi; + double step0 = lambda; + double step1 = ((nu + 1) * x / (x * x + nu)) * (lambda * lambda / 4.0); + + double step = step0; + + if (fabs (step1) < fabs (step0)) + { + step += step1; + } + + if (Q < 0.5 && x + step < 0) + x /= 2; + else if (Q > 0.5 && x + step > 0) + x /= 2; + else + x += step; + + if (fabs (step) > 1e-10 * fabs (x)) + goto start; + } + } + +end: + + return x; +} |