/*************************************************************************
Functional inverse of Student's t distribution
Given probability p, finds the argument t such that stdtr(k,t)
is equal to p.
ACCURACY:
Tested at random 1 <= k <= 100. The "domain" refers to p:
Relative error:
arithmetic domain # trials peak rms
IEEE .001,.999 25000 5.7e-15 8.0e-16
IEEE 10^-6,.001 25000 2.0e-12 2.9e-14
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
*************************************************************************/
double invstudenttdistribution(int k, double p)
{
double result;
double t;
double rk;
double z;
int rflg;
ap::ap_error::make_assertion(k>0&&p>0&&p<1);
rk = k;
if( p>0.25&&p<0.75 )
{
if( p==0.5 )
{
result = 0;
return result;
}
z = 1.0-2.0*p;
z = invincompletebeta(0.5, 0.5*rk, fabs(z));
t = sqrt(rk*z/(1.0-z));
if( p<0.5 )
{
t = -t;
}
result = t;
return result;
}
rflg = -1;
if( p>=0.5 )
{
p = 1.0-p;
rflg = 1;
}
z = invincompletebeta(0.5*rk, 0.5, 2.0*p);
if( ap::maxrealnumber*z<rk )
{
result = rflg*ap::maxrealnumber;
return result;
}
t = sqrt(rk/z-rk);
result = rflg*t;
return result;
}
/*************************************************************************
Inverse binomial distribution
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
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
*************************************************************************/
double invbinomialdistribution(int k, int n, double y)
{
double result;
double dk;
double dn;
double p;
ap::ap_error::make_assertion(p>=0&&p<=1, "Domain error in InvBinomialDistribution");
ap::ap_error::make_assertion(k>=0&&k<n, "Domain error in InvBinomialDistribution");
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 = incompletebeta(dn, dk, 0.5);
if( p>0.5 )
{
p = invincompletebeta(dk, dn, 1.0-y);
}
else
{
p = 1.0-invincompletebeta(dn, dk, y);
}
}
result = p;
return result;
}
