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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 );
-}