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/* cdf/binomial.c
*
* Copyright (C) 2004 Jason H. Stover.
* Copyright (C) 2004 Giulio Bottazzi
*
* 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., 675 Mass Ave, Cambridge, MA 02139, USA.
*/
#include <config.h>
#include <math.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_cdf.h>
#include <gsl/gsl_sf_gamma.h>
#include "error.h"
/* Computes the cumulative distribution function for a binomial
random variable. For a binomial random variable X with n trials
and success probability p,
Pr( X <= k ) = Pr( Y >= p )
where Y is a beta random variable with parameters k+1 and n-k.
The binomial distribution has the form,
prob(k) = n!/(k!(n-k)!) * p^k (1-p)^(n-k) for k = 0, 1, ..., n
The cumulated distributions can be expressed in terms of normalized
incomplete beta functions (see Abramowitz & Stegun eq. 26.5.26 and
eq. 6.6.3).
Reference:
W. Feller, "An Introduction to Probability and Its
Applications," volume 1. Wiley, 1968. Exercise 45, page 173,
chapter 6.
*/
#include <config.h>
#include <math.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_cdf.h>
double
gsl_cdf_binomial_P (const unsigned int k, const double p, const unsigned int n)
{
double P;
double a;
double b;
if (p > 1.0 || p < 0.0)
{
CDF_ERROR ("p < 0 or p > 1", GSL_EDOM);
}
if (k >= n)
{
P = 1.0;
}
else
{
a = (double) k + 1.0;
b = (double) n - k;
P = gsl_cdf_beta_Q (p, a, b);
}
return P;
}
double
gsl_cdf_binomial_Q (const unsigned int k, const double p, const unsigned int n)
{
double Q;
double a;
double b;
if (p > 1.0 || p < 0.0)
{
CDF_ERROR ("p < 0 or p > 1", GSL_EDOM);
}
if (k >= n)
{
Q = 0.0;
}
else
{
a = (double) k + 1.0;
b = (double) n - k;
Q = gsl_cdf_beta_P (p, a, b);
}
return Q;
}
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