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Diffstat (limited to 'libm/double/bdtr.c')
| -rw-r--r-- | libm/double/bdtr.c | 263 |
1 files changed, 263 insertions, 0 deletions
diff --git a/libm/double/bdtr.c b/libm/double/bdtr.c new file mode 100644 index 000000000..a268c7a10 --- /dev/null +++ b/libm/double/bdtr.c @@ -0,0 +1,263 @@ +/* bdtr.c + * + * Binomial distribution + * + * + * + * SYNOPSIS: + * + * int k, n; + * double p, y, bdtr(); + * + * y = bdtr( k, n, p ); + * + * DESCRIPTION: + * + * Returns the sum of the terms 0 through k of the Binomial + * probability density: + * + * k + * -- ( n ) j n-j + * > ( ) p (1-p) + * -- ( j ) + * j=0 + * + * The terms are not summed directly; instead the incomplete + * beta integral is employed, according to the formula + * + * y = bdtr( k, n, p ) = incbet( n-k, k+1, 1-p ). + * + * The arguments must be positive, with p ranging from 0 to 1. + * + * ACCURACY: + * + * Tested at random points (a,b,p), with p between 0 and 1. + * + * a,b Relative error: + * arithmetic domain # trials peak rms + * For p between 0.001 and 1: + * IEEE 0,100 100000 4.3e-15 2.6e-16 + * See also incbet.c. + * + * ERROR MESSAGES: + * + * message condition value returned + * bdtr domain k < 0 0.0 + * n < k + * x < 0, x > 1 + */ + /* bdtrc() + * + * Complemented binomial distribution + * + * + * + * SYNOPSIS: + * + * int k, n; + * double p, y, bdtrc(); + * + * y = bdtrc( k, n, p ); + * + * DESCRIPTION: + * + * Returns the sum of the terms k+1 through n of the Binomial + * probability density: + * + * n + * -- ( n ) j n-j + * > ( ) p (1-p) + * -- ( j ) + * j=k+1 + * + * The terms are not summed directly; instead the incomplete + * beta integral is employed, according to the formula + * + * y = bdtrc( k, n, p ) = incbet( k+1, n-k, p ). + * + * The arguments must be positive, with p ranging from 0 to 1. + * + * ACCURACY: + * + * Tested at random points (a,b,p). + * + * a,b Relative error: + * arithmetic domain # trials peak rms + * For p between 0.001 and 1: + * IEEE 0,100 100000 6.7e-15 8.2e-16 + * For p between 0 and .001: + * IEEE 0,100 100000 1.5e-13 2.7e-15 + * + * ERROR MESSAGES: + * + * message condition value returned + * bdtrc domain x<0, x>1, n<k 0.0 + */ + /* bdtri() + * + * Inverse binomial distribution + * + * + * + * SYNOPSIS: + * + * int k, n; + * double p, y, bdtri(); + * + * p = bdtr( k, n, y ); + * + * DESCRIPTION: + * + * Finds the event probability p such that the sum of the + * terms 0 through k of the Binomial probability density + * is equal to the given cumulative probability y. + * + * This is accomplished using the inverse beta integral + * function and the relation + * + * 1 - p = incbi( n-k, k+1, y ). + * + * ACCURACY: + * + * Tested at random points (a,b,p). + * + * a,b Relative error: + * arithmetic domain # trials peak rms + * For p between 0.001 and 1: + * IEEE 0,100 100000 2.3e-14 6.4e-16 + * IEEE 0,10000 100000 6.6e-12 1.2e-13 + * For p between 10^-6 and 0.001: + * IEEE 0,100 100000 2.0e-12 1.3e-14 + * IEEE 0,10000 100000 1.5e-12 3.2e-14 + * See also incbi.c. + * + * ERROR MESSAGES: + * + * message condition value returned + * bdtri domain k < 0, n <= k 0.0 + * x < 0, x > 1 + */ + +/* bdtr() */ + + +/* +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 ); +extern double pow ( double, double ); +extern double log1p ( double ); +extern double expm1 ( double ); +#else +double incbet(), incbi(), pow(), log1p(), expm1(); +#endif + +double bdtrc( k, n, p ) +int k, n; +double p; +{ +double dk, dn; + +if( (p < 0.0) || (p > 1.0) ) + goto domerr; +if( k < 0 ) + return( 1.0 ); + +if( n < k ) + { +domerr: + mtherr( "bdtrc", DOMAIN ); + return( 0.0 ); + } + +if( k == n ) + return( 0.0 ); +dn = n - k; +if( k == 0 ) + { + if( p < .01 ) + dk = -expm1( dn * log1p(-p) ); + else + dk = 1.0 - pow( 1.0-p, dn ); + } +else + { + dk = k + 1; + dk = incbet( dk, dn, p ); + } +return( dk ); +} + + + +double bdtr( k, n, p ) +int k, n; +double p; +{ +double dk, dn; + +if( (p < 0.0) || (p > 1.0) ) + goto domerr; +if( (k < 0) || (n < k) ) + { +domerr: + mtherr( "bdtr", DOMAIN ); + return( 0.0 ); + } + +if( k == n ) + return( 1.0 ); + +dn = n - k; +if( k == 0 ) + { + dk = pow( 1.0-p, dn ); + } +else + { + dk = k + 1; + dk = incbet( dn, dk, 1.0 - p ); + } +return( dk ); +} + + +double bdtri( k, n, y ) +int k, n; +double y; +{ +double dk, dn, p; + +if( (y < 0.0) || (y > 1.0) ) + goto domerr; +if( (k < 0) || (n <= k) ) + { +domerr: + mtherr( "bdtri", DOMAIN ); + return( 0.0 ); + } + +dn = n - k; +if( k == 0 ) + { + if( y > 0.8 ) + p = -expm1( log1p(y-1.0) / dn ); + else + p = 1.0 - pow( y, 1.0/dn ); + } +else + { + dk = k + 1; + p = incbet( dn, dk, 0.5 ); + if( p > 0.5 ) + p = incbi( dk, dn, 1.0-y ); + else + p = 1.0 - incbi( dn, dk, y ); + } +return( p ); +} |