/* cdf/geometric.c
*
* Copyright (C) 2004 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.
*/
/*
* Pr(X <= n) for a negative binomial random variable X, i.e.,
* the probability of n or fewer failuers before success k.
*/
#include
#include
#include
#include
#include
#include
/*
* Pr (X <= n), i.e., the probability of n or fewer
* failures until the first success.
*/
double
gsl_cdf_geometric_P (const long n, const double p)
{
double P;
double a;
int i;
int m;
double sign = 1.0;
double tmp;
double term;
double q;
if(p > 1.0 || p < 0.0)
{
GSL_CDF_ERROR("p < 0 or p > 1",GSL_EDOM);
}
if ( n < 0 )
{
return 0.0;
}
q = 1.0 - p;
a = (double) n+1;
if( p < GSL_DBL_EPSILON )
{
/*
* 1.0 - pow(q,a) will overflow, so use
* a Taylor series.
*/
i = 2;
m = n+1;
term = exp(log(a) + log(p));
P = term;
while ( term > GSL_DBL_MIN && i < m)
{
term = exp (sign * gsl_sf_lnchoose(m,i) + i * log(p));
P += term;
i++;
sign = -sign;
}
}
else
{
P = 1.0 - pow ( q, a);
}
return P;
}
double
gsl_cdf_geometric_Q ( const long n, const double p)
{
double P;
double q;
double a;
if(p > 1.0 || p < 0.0)
{
GSL_CDF_ERROR("p < 0 or p > 1",GSL_EDOM);
}
if ( n < 0 )
{
P = 1.0;
}
else
{
a = (double) n+1;
q = 1.0 - p;
P = pow(q, a);
}
return P;
}