/usr/include/binomialdistr.h is in libalglib-dev 2.6.0-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
Contributors:
* Sergey Bochkanov (ALGLIB project). Translation from C to
pseudocode.
See subroutines comments for additional copyrights.
>>> SOURCE LICENSE >>>
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 (www.fsf.org); 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.
A copy of the GNU General Public License is available at
http://www.fsf.org/licensing/licenses
>>> END OF LICENSE >>>
*************************************************************************/
#ifndef _binomialdistr_h
#define _binomialdistr_h
#include "ap.h"
#include "ialglib.h"
#include "gammafunc.h"
#include "normaldistr.h"
#include "ibetaf.h"
#include "nearunityunit.h"
/*************************************************************************
Binomial distribution
Returns the sum of the terms 0 through k of the Binomial
probability density:
k
-- ( n ) j n-j
> ( ) p (1-p)
-- ( j )
j=0
The terms are not summed directly; instead the incomplete
beta integral is employed, according to the formula
y = bdtr( k, n, p ) = incbet( n-k, k+1, 1-p ).
The arguments must be positive, with p ranging from 0 to 1.
ACCURACY:
Tested at random points (a,b,p), with p between 0 and 1.
a,b Relative error:
arithmetic domain # trials peak rms
For p between 0.001 and 1:
IEEE 0,100 100000 4.3e-15 2.6e-16
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
*************************************************************************/
double binomialdistribution(int k, int n, double p);
/*************************************************************************
Complemented binomial distribution
Returns the sum of the terms k+1 through n of the Binomial
probability density:
n
-- ( n ) j n-j
> ( ) p (1-p)
-- ( j )
j=k+1
The terms are not summed directly; instead the incomplete
beta integral is employed, according to the formula
y = bdtrc( k, n, p ) = incbet( k+1, n-k, p ).
The arguments must be positive, with p ranging from 0 to 1.
ACCURACY:
Tested at random points (a,b,p).
a,b Relative error:
arithmetic domain # trials peak rms
For p between 0.001 and 1:
IEEE 0,100 100000 6.7e-15 8.2e-16
For p between 0 and .001:
IEEE 0,100 100000 1.5e-13 2.7e-15
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
*************************************************************************/
double binomialcdistribution(int k, int n, double p);
/*************************************************************************
Inverse binomial distribution
Finds the event probability p such that the sum of the
terms 0 through k of the Binomial probability density
is equal to the given cumulative probability y.
This is accomplished using the inverse beta integral
function and the relation
1 - p = incbi( n-k, k+1, y ).
ACCURACY:
Tested at random points (a,b,p).
a,b Relative error:
arithmetic domain # trials peak rms
For p between 0.001 and 1:
IEEE 0,100 100000 2.3e-14 6.4e-16
IEEE 0,10000 100000 6.6e-12 1.2e-13
For p between 10^-6 and 0.001:
IEEE 0,100 100000 2.0e-12 1.3e-14
IEEE 0,10000 100000 1.5e-12 3.2e-14
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
*************************************************************************/
double invbinomialdistribution(int k, int n, double y);
#endif
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