/usr/include/fdistr.h is in libalglib-dev 2.6.0-3.
This file is owned by root:root, with mode 0o644.
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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 _fdistr_h
#define _fdistr_h
#include "ap.h"
#include "ialglib.h"
#include "gammafunc.h"
#include "normaldistr.h"
#include "ibetaf.h"
/*************************************************************************
F distribution
Returns the area from zero to x under the F density
function (also known as Snedcor's density or the
variance ratio density). This is the density
of x = (u1/df1)/(u2/df2), where u1 and u2 are random
variables having Chi square distributions with df1
and df2 degrees of freedom, respectively.
The incomplete beta integral is used, according to the
formula
P(x) = incbet( df1/2, df2/2, (df1*x/(df2 + df1*x) ).
The arguments a and b are greater than zero, and x is
nonnegative.
ACCURACY:
Tested at random points (a,b,x).
x a,b Relative error:
arithmetic domain domain # trials peak rms
IEEE 0,1 0,100 100000 9.8e-15 1.7e-15
IEEE 1,5 0,100 100000 6.5e-15 3.5e-16
IEEE 0,1 1,10000 100000 2.2e-11 3.3e-12
IEEE 1,5 1,10000 100000 1.1e-11 1.7e-13
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
*************************************************************************/
double fdistribution(int a, int b, double x);
/*************************************************************************
Complemented F distribution
Returns the area from x to infinity under the F density
function (also known as Snedcor's density or the
variance ratio density).
inf.
-
1 | | a-1 b-1
1-P(x) = ------ | t (1-t) dt
B(a,b) | |
-
x
The incomplete beta integral is used, according to the
formula
P(x) = incbet( df2/2, df1/2, (df2/(df2 + df1*x) ).
ACCURACY:
Tested at random points (a,b,x) in the indicated intervals.
x a,b Relative error:
arithmetic domain domain # trials peak rms
IEEE 0,1 1,100 100000 3.7e-14 5.9e-16
IEEE 1,5 1,100 100000 8.0e-15 1.6e-15
IEEE 0,1 1,10000 100000 1.8e-11 3.5e-13
IEEE 1,5 1,10000 100000 2.0e-11 3.0e-12
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
*************************************************************************/
double fcdistribution(int a, int b, double x);
/*************************************************************************
Inverse of complemented F distribution
Finds the F density argument x such that the integral
from x to infinity of the F density is equal to the
given probability p.
This is accomplished using the inverse beta integral
function and the relations
z = incbi( df2/2, df1/2, p )
x = df2 (1-z) / (df1 z).
Note: the following relations hold for the inverse of
the uncomplemented F distribution:
z = incbi( df1/2, df2/2, p )
x = df2 z / (df1 (1-z)).
ACCURACY:
Tested at random points (a,b,p).
a,b Relative error:
arithmetic domain # trials peak rms
For p between .001 and 1:
IEEE 1,100 100000 8.3e-15 4.7e-16
IEEE 1,10000 100000 2.1e-11 1.4e-13
For p between 10^-6 and 10^-3:
IEEE 1,100 50000 1.3e-12 8.4e-15
IEEE 1,10000 50000 3.0e-12 4.8e-14
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
*************************************************************************/
double invfdistribution(int a, int b, double y);
#endif
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