| /* randist/lognormal.c |
| * |
| * Copyright (C) 1996, 1997, 1998, 1999, 2000 James Theiler, Brian Gough |
| * |
| * 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. |
| */ |
| |
| #include <config.h> |
| #include <math.h> |
| #include <gsl/gsl_math.h> |
| #include <gsl/gsl_rng.h> |
| #include <gsl/gsl_randist.h> |
| |
| /* The lognormal distribution has the form |
| |
| p(x) dx = 1/(x * sqrt(2 pi sigma^2)) exp(-(ln(x) - zeta)^2/2 sigma^2) dx |
| |
| for x > 0. Lognormal random numbers are the exponentials of |
| gaussian random numbers */ |
| |
| double |
| gsl_ran_lognormal (const gsl_rng * r, const double zeta, const double sigma) |
| { |
| double u, v, r2, normal, z; |
| |
| do |
| { |
| /* choose x,y in uniform square (-1,-1) to (+1,+1) */ |
| |
| u = -1 + 2 * gsl_rng_uniform (r); |
| v = -1 + 2 * gsl_rng_uniform (r); |
| |
| /* see if it is in the unit circle */ |
| r2 = u * u + v * v; |
| } |
| while (r2 > 1.0 || r2 == 0); |
| |
| normal = u * sqrt (-2.0 * log (r2) / r2); |
| |
| z = exp (sigma * normal + zeta); |
| |
| return z; |
| } |
| |
| double |
| gsl_ran_lognormal_pdf (const double x, const double zeta, const double sigma) |
| { |
| if (x <= 0) |
| { |
| return 0 ; |
| } |
| else |
| { |
| double u = (log (x) - zeta)/sigma; |
| double p = 1 / (x * fabs(sigma) * sqrt (2 * M_PI)) * exp (-(u * u) /2); |
| return p; |
| } |
| } |