// derived values
/// <summary>
/// Constructs a F-distribution with
/// the given degrees of freedom.
/// </summary>
/// <param name="degrees1">The first degree of freedom.</param>
/// <param name="degrees2">The second degree of freedom.</param>
public FDistribution(int degrees1, int degrees2)
{
d1 = degrees1;
d2 = degrees2;
b = Special.Beta(degrees1 * 0.5, degrees2 * 0.5);
}
/// <summary>
/// Constructs a F-distribution with
/// the given degrees of freedom.
/// </summary>
///
/// <param name="degrees1">The first degree of freedom.</param>
/// <param name="degrees2">The second degree of freedom.</param>
///
public FDistribution(int degrees1, int degrees2)
{
this.d1 = degrees1;
this.d2 = degrees2;
this.b = Special.Beta(degrees1 * 0.5, degrees2 * 0.5);
}
/// <summary>
/// Returns the value of the probability density function.
/// </summary>
/// <param name="x">Value</param>
/// <returns>float precision floating point number</returns>
public float Function(float x)
{
// helpers:
float d12 = d1 / 2.0f;
float d22 = d2 / 2.0f;
// first equation:
float a = (float)Math.Pow(d1, d12);
float b = (float)Math.Pow(d2, d22);
float c = 2 * a * b;
float d = Special.Beta(d12, d22);
float e = c / d;
// second equation:
float f = (float)Math.Exp(d1 * x);
float g = d1 * (float)Math.Exp(2 * x) + d2;
float h = d12 + d22;
float j = f / (float)Math.Pow(g, h);
// result of F(x, d1, d2):
return(e * j);
}
/// <summary>
/// Returns the value of the probability distribution function.
/// </summary>
/// <param name="x">Value</param>
/// <returns>float precision floating point number</returns>
public float Distribution(float x)
{
if (x > 1)
{
return(0);
}
else if (x < 0)
{
return(0);
}
return(Special.Beta(a, b, x));
}
/// <summary>
/// Returns the value of the probability density function.
/// </summary>
/// <param name="x">Value</param>
/// <returns>float precision floating point number</returns>
public float Function(float x)
{
if (x > 1)
{
return(0);
}
else if (x < 0)
{
return(0);
}
return((float)Math.Pow(x, a - 1) * (float)Math.Pow(1 - x, b - 1) / Special.Beta(a, b));
}
/// <summary>
/// Returns the value of the probability density function.
/// </summary>
/// <param name="x">Value</param>
/// <returns>float precision floating point number</returns>
public float Function(float x)
{
if (x <= 0)
{
return(0);
}
float num = (float)Math.Pow(x, alpha - 1) * (float)Math.Pow(1 + x, -alpha - beta);
float den = Special.Beta(alpha, beta);
return(num / den);
}
/// <summary>
/// Returns the value of the probability distribution function.
/// </summary>
/// <param name="x">Value</param>
/// <returns>float precision floating point number</returns>
public float Distribution(float x)
{
if (x <= 0)
{
return(0);
}
if (x > 1)
{
return(0);
}
return(1 + Special.Beta(x + 1, 0) / (float)Math.Log(1 - p));
}
/// <summary>
/// Returns the value of the probability distribution function.
/// </summary>
/// <param name="x">Value</param>
/// <returns>float precision floating point number</returns>
public float Distribution(float x)
{
if (x < 0)
{
return(0);
}
if (x >= n)
{
return(1);
}
float a = n - x;
float b = x + 1;
return(Special.Beta(a, b, q));
}
/// <summary>
/// Initializes the Fisher distribution.
/// </summary>
/// <param name="d1">First degree of freedom</param>
/// <param name="d2">Second degree of freedom</param>
public FisherSnedecor(int d1 = 1, int d2 = 1)
{
if (d1 <= 0)
{
throw new ArgumentOutOfRangeException("d1", "The value must be greater than zero.");
}
if (d2 <= 0)
{
throw new ArgumentOutOfRangeException("d2", "The value must be greater than zero.");
}
this.d1 = d1;
this.d2 = d2;
this.b = Special.Beta(d1 * 0.5f, d2 * 0.5f);
}
/// <summary>
///
/// </summary>
/// <param name="n"></param>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
protected static float momentGeneratingFunction(int n, float a, float b)
{
return(b * Special.Beta(1.0f + ((float)n) / a, b));
}