/* chdtr.c * * Chi-square distribution * * * * SYNOPSIS: * * double df, x, y, chdtr(); * * y = chdtr( 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 */ /* chdtrc() * * Complemented Chi-square distribution * * * * SYNOPSIS: * * double v, x, y, chdtrc(); * * y = chdtrc( 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 */ /* chdtri() * * Inverse of complemented Chi-square distribution * * * * SYNOPSIS: * * double df, x, y, chdtri(); * * x = chdtri( 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 2.8: June, 2000 Copyright 1984, 1987, 2000 by Stephen L. Moshier */ #include <math.h> #ifdef ANSIPROT extern double igamc ( double, double ); extern double igam ( double, double ); extern double igami ( double, double ); #else double igamc(), igam(), igami(); #endif double chdtrc(df,x) double df, x; { if( (x < 0.0) || (df < 1.0) ) { mtherr( "chdtrc", DOMAIN ); return(0.0); } return( igamc( df/2.0, x/2.0 ) ); } double chdtr(df,x) double df, x; { if( (x < 0.0) || (df < 1.0) ) { mtherr( "chdtr", DOMAIN ); return(0.0); } return( igam( df/2.0, x/2.0 ) ); } double chdtri( df, y ) double df, y; { double x; if( (y < 0.0) || (y > 1.0) || (df < 1.0) ) { mtherr( "chdtri", DOMAIN ); return(0.0); } x = igami( 0.5 * df, y ); return( 2.0 * x ); }