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/* chdtrl.c
*
* Chi-square distribution
*
*
*
* SYNOPSIS:
*
* long double df, x, y, chdtrl();
*
* y = chdtrl( 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:
*
* See igam().
*
* ERROR MESSAGES:
*
* message condition value returned
* chdtr domain x < 0 or v < 1 0.0
*/
/* chdtrcl()
*
* Complemented Chi-square distribution
*
*
*
* SYNOPSIS:
*
* long double v, x, y, chdtrcl();
*
* y = chdtrcl( 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:
*
* See igamc().
*
* ERROR MESSAGES:
*
* message condition value returned
* chdtrc domain x < 0 or v < 1 0.0
*/
/* chdtril()
*
* Inverse of complemented Chi-square distribution
*
*
*
* SYNOPSIS:
*
* long double df, x, y, chdtril();
*
* x = chdtril( 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:
*
* See igami.c.
*
* ERROR MESSAGES:
*
* message condition value returned
* chdtri domain y < 0 or y > 1 0.0
* v < 1
*
*/
/* chdtr() */
/*
Cephes Math Library Release 2.3: March, 1995
Copyright 1984, 1995 by Stephen L. Moshier
*/
#include <math.h>
#ifdef ANSIPROT
extern long double igamcl ( long double, long double );
extern long double igaml ( long double, long double );
extern long double igamil ( long double, long double );
#else
long double igamcl(), igaml(), igamil();
#endif
long double chdtrcl(df,x)
long double df, x;
{
if( (x < 0.0L) || (df < 1.0L) )
{
mtherr( "chdtrcl", DOMAIN );
return(0.0L);
}
return( igamcl( 0.5L*df, 0.5L*x ) );
}
long double chdtrl(df,x)
long double df, x;
{
if( (x < 0.0L) || (df < 1.0L) )
{
mtherr( "chdtrl", DOMAIN );
return(0.0L);
}
return( igaml( 0.5L*df, 0.5L*x ) );
}
long double chdtril( df, y )
long double df, y;
{
long double x;
if( (y < 0.0L) || (y > 1.0L) || (df < 1.0L) )
{
mtherr( "chdtril", DOMAIN );
return(0.0L);
}
x = igamil( 0.5L * df, y );
return( 2.0L * x );
}
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