/*************************************************************************
Chi-square distribution
Returns the area under the left hand tail (from 0 to x)
of the Chi square probability density function with
v degrees of freedom.
x
-
1 | | v/2-1 -t/2
P( x | v ) = ----------- | t e dt
v/2 - | |
2 | (v/2) -
0
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 incomplete gamma function
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 2000 by Stephen L. Moshier
*************************************************************************/
double chisquaredistribution(double v, double x)
{
double result;
ap::ap_error::make_assertion(ap::fp_greater_eq(x,0)&&ap::fp_greater_eq(v,1), "Domain error in ChiSquareDistribution");
result = incompletegamma(v/2.0, x/2.0);
return result;
}
/*************************************************************************
Complemented incomplete gamma integral
The function is defined by
igamc(a,x) = 1 - igam(a,x)
inf.
-
1 | | -t a-1
= ----- | e t dt.
- | |
| (a) -
x
In this implementation both arguments must be positive.
The integral is evaluated by either a power series or
continued fraction expansion, depending on the relative
values of a and x.
ACCURACY:
Tested at random a, x.
a x Relative error:
arithmetic domain domain # trials peak rms
IEEE 0.5,100 0,100 200000 1.9e-14 1.7e-15
IEEE 0.01,0.5 0,100 200000 1.4e-13 1.6e-15
Cephes Math Library Release 2.8: June, 2000
Copyright 1985, 1987, 2000 by Stephen L. Moshier
*************************************************************************/
double incompletegammac(double a, double x)
{
double result;
double igammaepsilon;
double igammabignumber;
double igammabignumberinv;
double ans;
double ax;
double c;
double yc;
double r;
double t;
double y;
double z;
double pk;
double pkm1;
double pkm2;
double qk;
double qkm1;
double qkm2;
double tmp;
igammaepsilon = 0.000000000000001;
igammabignumber = 4503599627370496.0;
igammabignumberinv = 2.22044604925031308085*0.0000000000000001;
if( ap::fp_less_eq(x,0)||ap::fp_less_eq(a,0) )
{
result = 1;
return result;
}
if( ap::fp_less(x,1)||ap::fp_less(x,a) )
{
result = 1-incompletegamma(a, x);
return result;
}
ax = a*log(x)-x-lngamma(a, tmp);
if( ap::fp_less(ax,-709.78271289338399) )
{
result = 0;
return result;
}
ax = exp(ax);
y = 1-a;
z = x+y+1;
c = 0;
pkm2 = 1;
qkm2 = x;
pkm1 = x+1;
qkm1 = z*x;
ans = pkm1/qkm1;
do
{
c = c+1;
y = y+1;
z = z+2;
yc = y*c;
pk = pkm1*z-pkm2*yc;
qk = qkm1*z-qkm2*yc;
if( ap::fp_neq(qk,0) )
{
r = pk/qk;
t = fabs((ans-r)/r);
ans = r;
}
else
{
t = 1;
}
pkm2 = pkm1;
pkm1 = pk;
qkm2 = qkm1;
qkm1 = qk;
if( ap::fp_greater(fabs(pk),igammabignumber) )
{
pkm2 = pkm2*igammabignumberinv;
pkm1 = pkm1*igammabignumberinv;
qkm2 = qkm2*igammabignumberinv;
qkm1 = qkm1*igammabignumberinv;
}
}
while(ap::fp_greater(t,igammaepsilon));
result = ans*ax;
return result;
}
