/// <summary>
/// Gets the cumulative distribution function (cdf) for
/// the this distribution evaluated at point <c>x</c>.
/// </summary>
///
/// <param name="x">A single point in the distribution range.</param>
///
/// <remarks>
/// The Cumulative Distribution Function (CDF) describes the cumulative
/// probability that a given value or any value smaller than it will occur.
/// </remarks>
///
public override double DistributionFunction(double x)
{
double v = DegreesOfFreedom;
double sqrt = Math.Sqrt(x * x + v);
double u = (x + sqrt) / (2 * sqrt);
return(Special.Ibeta(v / 2.0, v / 2.0, u));
}
/// <summary>
/// Gets the cumulative distribution function (cdf) for
/// the F-distribution evaluated at point <c>x</c>.
/// </summary>
///
/// <param name="x">A single point in the distribution range.</param>
///
/// <remarks>
/// The Cumulative Distribution Function (CDF) describes the cumulative
/// probability that a given value or any value smaller than it will occur.
/// </remarks>
///
public override double DistributionFunction(double x)
{
double u = (d1 * x) / (d1 * x + d2);
return(Special.Ibeta(d1 * 0.5, d2 * 0.5, u));
}