/* 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 ); }