/* 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 ); }