1 /* randist/lognormal.c
2 *
3 * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 James Theiler, Brian Gough
4 *
5 * This program is free software; you can redistribute it and/or modify
6 * it under the terms of the GNU General Public License as published by
7 * the Free Software Foundation; either version 3 of the License, or (at
8 * your option) any later version.
9 *
10 * This program is distributed in the hope that it will be useful, but
11 * WITHOUT ANY WARRANTY; without even the implied warranty of
12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 * General Public License for more details.
14 *
15 * You should have received a copy of the GNU General Public License
16 * along with this program; if not, write to the Free Software
17 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
18 */
19
20 #include "gsl__config.h"
21 #include <math.h>
22 #include "gsl_math.h"
23 #include "gsl_rng.h"
24 #include "gsl_randist.h"
25
26 /* The lognormal distribution has the form
27
28 p(x) dx = 1/(x * sqrt(2 pi sigma^2)) exp(-(ln(x) - zeta)^2/2 sigma^2) dx
29
30 for x > 0. Lognormal random numbers are the exponentials of
31 gaussian random numbers */
32
33 double
gsl_ran_lognormal(const gsl_rng * r,const double zeta,const double sigma)34 gsl_ran_lognormal (const gsl_rng * r, const double zeta, const double sigma)
35 {
36 double u, v, r2, normal, z;
37
38 do
39 {
40 /* choose x,y in uniform square (-1,-1) to (+1,+1) */
41
42 u = -1 + 2 * gsl_rng_uniform (r);
43 v = -1 + 2 * gsl_rng_uniform (r);
44
45 /* see if it is in the unit circle */
46 r2 = u * u + v * v;
47 }
48 while (r2 > 1.0 || r2 == 0);
49
50 normal = u * sqrt (-2.0 * log (r2) / r2);
51
52 z = exp (sigma * normal + zeta);
53
54 return z;
55 }
56
57 double
gsl_ran_lognormal_pdf(const double x,const double zeta,const double sigma)58 gsl_ran_lognormal_pdf (const double x, const double zeta, const double sigma)
59 {
60 if (x <= 0)
61 {
62 return 0 ;
63 }
64 else
65 {
66 double u = (log (x) - zeta)/sigma;
67 double p = 1 / (x * fabs(sigma) * sqrt (2 * M_PI)) * exp (-(u * u) /2);
68 return p;
69 }
70 }
71