/// <summary>
/// ACM Algorithm 395: Student's t-distribution
///
/// Evaluates the two-tail probability P(t|n) that t is exceeded
/// in magnitude for Student's t-distribution with n degrees of freedom.
///
/// http://dl.acm.org/citation.cfm?id=355599
/// </summary>
/// <param name="t">t-value, t > 0</param>
/// <param name="n">Degree of freedom, n >= 1</param>
/// <returns>2-tail p-value</returns>
public static double StudentTwoTail(double t, double n)
{
if (t < 0)
{
throw new ArgumentOutOfRangeException(nameof(t), "t should be >= 0");
}
if (n < 1)
{
throw new ArgumentOutOfRangeException(nameof(n), "n should be >= 1");
}
t = t.Sqr();
double y = t / n;
double b = y + 1.0;
int nn = (int)Round(n);
if (Abs(n - nn) > 1e-9 || n >= 20 || t < n && n > 200)
{
if (y > 1.0e-6)
{
y = Log(b);
}
double a = n - 0.5;
b = 48.0 * a.Sqr();
y = a * y;
y = (((((-0.4 * y - 3.3) * y - 24.0) * y - 85.5) / (0.8 * y.Sqr() + 100.0 + b) + y + 3.0) / b + 1.0) * Sqrt(y);
return(2 * NormalDistribution.Gauss(-y));
}
{
double z = 1;
double a;
if (n < 20 && t < 4.0)
{
y = Sqrt(y);
a = y;
if (nn == 1)
{
a = 0;
}
}
else
{
a = Sqrt(b);
y = a * nn;
int j = 0;
while (Abs(a - z) > 0)
{
j += 2;
z = a;
y *= (j - 1) / (b * j);
a += y / (nn + j);
}
nn += 2;
z = 0;
y = 0;
a = -a;
}
while (true)
{
nn -= 2;
if (nn > 1)
{
a = (nn - 1) / (b * nn) * a + y;
}
else
{
break;
}
}
a = nn == 0 ? a / Sqrt(b) : (Atan(y) + a / b) * 2 / PI;
return(z - a);
}
}
public NormalRandomGenerator(int seed, NormalDistribution distribution) : base(seed)
{
this.distribution = distribution;
}
public NormalRandomGenerator(Random random, NormalDistribution distribution) : base(random)
{
this.distribution = distribution;
}
public NormalRandomGenerator(NormalDistribution distribution)
{
this.distribution = distribution;
}
