/// <summary>
/// Returns the CDF of the F distribution.
/// </summary>
/// <param name="x">Value at which the distribution is evaluated.</param>
/// <param name="k1">Degrees of freedom for numerator chi-sqared distribution.</param>
/// <param name="k2">Degrees of freedom for denominator chi-sqared distribution.</param>
public static double FCumulativeDensityFunction(double x, int k1, int k2)
{
//Tested against Excel for
//k1 & k2 = 1, 2, 3, ... , 9, 10, 20, ... , 100
//x = 0.0, 0.1, 0.2, ... , 6.0
//maximum discrepancy was less than 0.16% for (x, k1, k2) = (6, 1, 9)
if (k1 <= 0 || k2 <= 0)
{
throw new ArgumentException("k1 and k2 must be greater than 0.");
}
if (x < 0)
{
throw new ArgumentException("x must be greater than 0.");
}
if (x == 0)
{
return(0.0);
}
double x2 = (k1 * x) / (k1 * x + k2);
double p = MMath.RegularizedIncompleteBetaFunction(x2, 0.5 * k1, 0.5 * k2);
return(Math.Min(1, p));
}
/// <summary>
/// Returns the CDF of a beta distribution with shape parameters a and b.
/// PDF is: f(x) = x^(a-1) * (1-x)^(b-1) / B(a,b)
/// </summary>
/// <param name="x">Value of the random variable for which the CDF is beign evaluated. x is between 0 and 1.</param>
/// <param name="a">First shape parameter.</param>
/// <param name="b">Second shape parameter.</param>
/// <returns></returns>
public static double BetaCumulativeDistributionFunction(double x, double a, double b)
{
if (x < 0 || x > 1)
{
throw new ArgumentException("x must be between 0 and 1");
}
return(MMath.RegularizedIncompleteBetaFunction(x, a, b));
}
/// <summary>
/// Returns the CDF of Student's t distribution.
/// </summary>
/// <param name="x">Value at which the distribution is evaluated.</param>
/// <param name="k">Degrees of freedom.</param>
public static double StudentsTCumulativeDensityFunction(double x, double k)
{
//Tested against Excel for
//df = 1, 2, 3, 4, 5, 10, 20, 30, 40, 50, 100, 200, 30, 400, 500 and
//x = -7.0, -6.9, -6.8, ..., 7.0
//maximum discrepancy was less than 0.04%
if (double.IsNaN(x))
{
return(double.NaN);
}
if (x == 0)
{
return(0.5);
}
if (x > 0)
{
double x2 = k / (x * x + k);
return(1.0 - 0.5 * MMath.RegularizedIncompleteBetaFunction(x2, 0.5 * k, 0.5));
}
return(1.0 - StudentsTCumulativeDensityFunction(-x, k));
}