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/* fdtrf.c
*
* F distribution
*
*
*
* SYNOPSIS:
*
* int df1, df2;
* float x, y, fdtrf();
*
* y = fdtrf( df1, df2, x );
*
*
*
* DESCRIPTION:
*
* 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
* x is nonnegative.
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0,100 5000 2.2e-5 1.1e-6
*
* ERROR MESSAGES:
*
* message condition value returned
* fdtrf domain a<0, b<0, x<0 0.0
*
*/
/* fdtrcf()
*
* Complemented F distribution
*
*
*
* SYNOPSIS:
*
* int df1, df2;
* float x, y, fdtrcf();
*
* y = fdtrcf( df1, df2, x );
*
*
*
* DESCRIPTION:
*
* 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
*
* (See fdtr.c.)
*
* The incomplete beta integral is used, according to the
* formula
*
* P(x) = incbet( df2/2, df1/2, (df2/(df2 + df1*x) ).
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0,100 5000 7.3e-5 1.2e-5
*
* ERROR MESSAGES:
*
* message condition value returned
* fdtrcf domain a<0, b<0, x<0 0.0
*
*/
/* fdtrif()
*
* Inverse of complemented F distribution
*
*
*
* SYNOPSIS:
*
* float df1, df2, x, y, fdtrif();
*
* x = fdtrif( df1, df2, y );
*
*
*
*
* DESCRIPTION:
*
* Finds the F density argument x such that the integral
* from x to infinity of the F density is equal to the
* given probability y.
*
* This is accomplished using the inverse beta integral
* function and the relations
*
* z = incbi( df2/2, df1/2, y )
* 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, y )
* x = df2 z / (df1 (1-z)).
*
*
*
* ACCURACY:
*
* arithmetic domain # trials peak rms
* Absolute error:
* IEEE 0,100 5000 4.0e-5 3.2e-6
* Relative error:
* IEEE 0,100 5000 1.2e-3 1.8e-5
*
* ERROR MESSAGES:
*
* message condition value returned
* fdtrif domain y <= 0 or y > 1 0.0
* v < 1
*
*/
/*
Cephes Math Library Release 2.2: July, 1992
Copyright 1984, 1987, 1992 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
#include <math.h>
#ifdef ANSIC
float incbetf(float, float, float);
float incbif(float, float, float);
#else
float incbetf(), incbif();
#endif
float fdtrcf( int ia, int ib, float xx )
{
float x, a, b, w;
x = xx;
if( (ia < 1) || (ib < 1) || (x < 0.0) )
{
mtherr( "fdtrcf", DOMAIN );
return( 0.0 );
}
a = ia;
b = ib;
w = b / (b + a * x);
return( incbetf( 0.5*b, 0.5*a, w ) );
}
float fdtrf( int ia, int ib, int xx )
{
float x, a, b, w;
x = xx;
if( (ia < 1) || (ib < 1) || (x < 0.0) )
{
mtherr( "fdtrf", DOMAIN );
return( 0.0 );
}
a = ia;
b = ib;
w = a * x;
w = w / (b + w);
return( incbetf( 0.5*a, 0.5*b, w) );
}
float fdtrif( int ia, int ib, float yy )
{
float y, a, b, w, x;
y = yy;
if( (ia < 1) || (ib < 1) || (y <= 0.0) || (y > 1.0) )
{
mtherr( "fdtrif", DOMAIN );
return( 0.0 );
}
a = ia;
b = ib;
w = incbif( 0.5*b, 0.5*a, y );
x = (b - b*w)/(a*w);
return(x);
}
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