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Diffstat (limited to 'libm/double/fdtr.c')
| -rw-r--r-- | libm/double/fdtr.c | 237 |
1 files changed, 0 insertions, 237 deletions
diff --git a/libm/double/fdtr.c b/libm/double/fdtr.c deleted file mode 100644 index 469b7bedf..000000000 --- a/libm/double/fdtr.c +++ /dev/null @@ -1,237 +0,0 @@ -/* fdtr.c - * - * F distribution - * - * - * - * SYNOPSIS: - * - * int df1, df2; - * double x, y, fdtr(); - * - * y = fdtr( df1, df2, x ); - * - * DESCRIPTION: - * - * Returns the area from zero to x under the F density - * function (also known as Snedcor's density or the - * variance ratio density). This is the density - * of x = (u1/df1)/(u2/df2), where u1 and u2 are random - * variables having Chi square distributions with df1 - * and df2 degrees of freedom, respectively. - * - * The incomplete beta integral is used, according to the - * formula - * - * P(x) = incbet( df1/2, df2/2, (df1*x/(df2 + df1*x) ). - * - * - * The arguments a and b are greater than zero, and x is - * nonnegative. - * - * ACCURACY: - * - * Tested at random points (a,b,x). - * - * x a,b Relative error: - * arithmetic domain domain # trials peak rms - * IEEE 0,1 0,100 100000 9.8e-15 1.7e-15 - * IEEE 1,5 0,100 100000 6.5e-15 3.5e-16 - * IEEE 0,1 1,10000 100000 2.2e-11 3.3e-12 - * IEEE 1,5 1,10000 100000 1.1e-11 1.7e-13 - * See also incbet.c. - * - * - * ERROR MESSAGES: - * - * message condition value returned - * fdtr domain a<0, b<0, x<0 0.0 - * - */ - /* fdtrc() - * - * Complemented F distribution - * - * - * - * SYNOPSIS: - * - * int df1, df2; - * double x, y, fdtrc(); - * - * y = fdtrc( df1, df2, x ); - * - * DESCRIPTION: - * - * Returns the area from x to infinity under the F density - * function (also known as Snedcor's density or the - * variance ratio density). - * - * - * inf. - * - - * 1 | | a-1 b-1 - * 1-P(x) = ------ | t (1-t) dt - * B(a,b) | | - * - - * x - * - * - * The incomplete beta integral is used, according to the - * formula - * - * P(x) = incbet( df2/2, df1/2, (df2/(df2 + df1*x) ). - * - * - * ACCURACY: - * - * Tested at random points (a,b,x) in the indicated intervals. - * x a,b Relative error: - * arithmetic domain domain # trials peak rms - * IEEE 0,1 1,100 100000 3.7e-14 5.9e-16 - * IEEE 1,5 1,100 100000 8.0e-15 1.6e-15 - * IEEE 0,1 1,10000 100000 1.8e-11 3.5e-13 - * IEEE 1,5 1,10000 100000 2.0e-11 3.0e-12 - * See also incbet.c. - * - * ERROR MESSAGES: - * - * message condition value returned - * fdtrc domain a<0, b<0, x<0 0.0 - * - */ - /* fdtri() - * - * Inverse of complemented F distribution - * - * - * - * SYNOPSIS: - * - * int df1, df2; - * double x, p, fdtri(); - * - * x = fdtri( df1, df2, p ); - * - * DESCRIPTION: - * - * Finds the F density argument x such that the integral - * from x to infinity of the F density is equal to the - * given probability p. - * - * This is accomplished using the inverse beta integral - * function and the relations - * - * z = incbi( df2/2, df1/2, p ) - * x = df2 (1-z) / (df1 z). - * - * Note: the following relations hold for the inverse of - * the uncomplemented F distribution: - * - * z = incbi( df1/2, df2/2, p ) - * x = df2 z / (df1 (1-z)). - * - * ACCURACY: - * - * Tested at random points (a,b,p). - * - * a,b Relative error: - * arithmetic domain # trials peak rms - * For p between .001 and 1: - * IEEE 1,100 100000 8.3e-15 4.7e-16 - * IEEE 1,10000 100000 2.1e-11 1.4e-13 - * For p between 10^-6 and 10^-3: - * IEEE 1,100 50000 1.3e-12 8.4e-15 - * IEEE 1,10000 50000 3.0e-12 4.8e-14 - * See also fdtrc.c. - * - * ERROR MESSAGES: - * - * message condition value returned - * fdtri domain p <= 0 or p > 1 0.0 - * v < 1 - * - */ - - -/* -Cephes Math Library Release 2.8: June, 2000 -Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier -*/ - - -#include <math.h> -#ifdef ANSIPROT -extern double incbet ( double, double, double ); -extern double incbi ( double, double, double ); -#else -double incbet(), incbi(); -#endif - -double fdtrc( ia, ib, x ) -int ia, ib; -double x; -{ -double a, b, w; - -if( (ia < 1) || (ib < 1) || (x < 0.0) ) - { - mtherr( "fdtrc", DOMAIN ); - return( 0.0 ); - } -a = ia; -b = ib; -w = b / (b + a * x); -return( incbet( 0.5*b, 0.5*a, w ) ); -} - - - -double fdtr( ia, ib, x ) -int ia, ib; -double x; -{ -double a, b, w; - -if( (ia < 1) || (ib < 1) || (x < 0.0) ) - { - mtherr( "fdtr", DOMAIN ); - return( 0.0 ); - } -a = ia; -b = ib; -w = a * x; -w = w / (b + w); -return( incbet(0.5*a, 0.5*b, w) ); -} - - -double fdtri( ia, ib, y ) -int ia, ib; -double y; -{ -double a, b, w, x; - -if( (ia < 1) || (ib < 1) || (y <= 0.0) || (y > 1.0) ) - { - mtherr( "fdtri", DOMAIN ); - return( 0.0 ); - } -a = ia; -b = ib; -/* Compute probability for x = 0.5. */ -w = incbet( 0.5*b, 0.5*a, 0.5 ); -/* If that is greater than y, then the solution w < .5. - Otherwise, solve at 1-y to remove cancellation in (b - b*w). */ -if( w > y || y < 0.001) - { - w = incbi( 0.5*b, 0.5*a, y ); - x = (b - b*w)/(a*w); - } -else - { - w = incbi( 0.5*a, 0.5*b, 1.0-y ); - x = b*w/(a*(1.0-w)); - } -return(x); -} |