public static double StudentDistribution(int k, double t)
{
if (Math.Abs(t - 0) < Eps)
{
return(.5);
}
if (t < -2)
{
return(.5 * IncompleteBeta.IncompleteBetaValue(.5 * k, .5, k / (k + t * t)));
}
var x = t < 0 ? -t : t;
double rk = k;
var z = 1 + x * x / rk;
double tz;
double f;
double p;
int j;
if (k % 2 != 0)
{
var x_sqk = x / Math.Sqrt(rk);
p = Math.Atan(x_sqk);
if (k > 1)
{
f = 1;
tz = 1;
j = 3;
while (j <= k - 2 & tz / f > Eps)
{
tz *= (j - 1) / (z * j);
f += tz;
j += 2;
}
p += f * x_sqk / z;
}
p *= 2 / Consts.pi;
}
else
{
f = tz = 1;
j = 2;
while (j <= k - 2 & tz / f > Eps)
{
tz *= (j - 1) / (z * j);
f += tz;
j += 2;
}
p = f * x / Math.Sqrt(z * rk);
}
return(.5 + .5 * (t < 0 ? -p : p));
}
