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/* chdtrf.c
*
* Chi-square distribution
*
*
*
* SYNOPSIS:
*
* float df, x, y, chdtrf();
*
* y = chdtrf( df, x );
*
*
*
* DESCRIPTION:
*
* Returns the area under the left hand tail (from 0 to x)
* of the Chi square probability density function with
* v degrees of freedom.
*
*
* inf.
* -
* 1 | | v/2-1 -t/2
* P( x | v ) = ----------- | t e dt
* v/2 - | |
* 2 | (v/2) -
* x
*
* where x is the Chi-square variable.
*
* The incomplete gamma integral is used, according to the
* formula
*
* y = chdtr( v, x ) = igam( v/2.0, x/2.0 ).
*
*
* The arguments must both be positive.
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0,100 5000 3.2e-5 5.0e-6
*
* ERROR MESSAGES:
*
* message condition value returned
* chdtrf domain x < 0 or v < 1 0.0
*/
/* chdtrcf()
*
* Complemented Chi-square distribution
*
*
*
* SYNOPSIS:
*
* float v, x, y, chdtrcf();
*
* y = chdtrcf( v, x );
*
*
*
* DESCRIPTION:
*
* Returns the area under the right hand tail (from x to
* infinity) of the Chi square probability density function
* with v degrees of freedom:
*
*
* inf.
* -
* 1 | | v/2-1 -t/2
* P( x | v ) = ----------- | t e dt
* v/2 - | |
* 2 | (v/2) -
* x
*
* where x is the Chi-square variable.
*
* The incomplete gamma integral is used, according to the
* formula
*
* y = chdtr( v, x ) = igamc( v/2.0, x/2.0 ).
*
*
* The arguments must both be positive.
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0,100 5000 2.7e-5 3.2e-6
*
* ERROR MESSAGES:
*
* message condition value returned
* chdtrc domain x < 0 or v < 1 0.0
*/
/* chdtrif()
*
* Inverse of complemented Chi-square distribution
*
*
*
* SYNOPSIS:
*
* float df, x, y, chdtrif();
*
* x = chdtrif( df, y );
*
*
*
*
* DESCRIPTION:
*
* Finds the Chi-square argument x such that the integral
* from x to infinity of the Chi-square density is equal
* to the given cumulative probability y.
*
* This is accomplished using the inverse gamma integral
* function and the relation
*
* x/2 = igami( df/2, y );
*
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0,100 10000 2.2e-5 8.5e-7
*
* ERROR MESSAGES:
*
* message condition value returned
* chdtri domain y < 0 or y > 1 0.0
* v < 1
*
*/
/* chdtr() */
/*
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 igamcf(float, float), igamf(float, float), igamif(float, float);
#else
float igamcf(), igamf(), igamif();
#endif
float chdtrcf(float dff, float xx)
{
float df, x;
df = dff;
x = xx;
if( (x < 0.0) || (df < 1.0) )
{
mtherr( "chdtrcf", DOMAIN );
return(0.0);
}
return( igamcf( 0.5*df, 0.5*x ) );
}
float chdtrf(float dff, float xx)
{
float df, x;
df = dff;
x = xx;
if( (x < 0.0) || (df < 1.0) )
{
mtherr( "chdtrf", DOMAIN );
return(0.0);
}
return( igamf( 0.5*df, 0.5*x ) );
}
float chdtrif( float dff, float yy )
{
float y, df, x;
y = yy;
df = dff;
if( (y < 0.0) || (y > 1.0) || (df < 1.0) )
{
mtherr( "chdtrif", DOMAIN );
return(0.0);
}
x = igamif( 0.5 * df, y );
return( 2.0 * x );
}
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