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-/* 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);
-}