/// <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);
}
return(0.5f + 0.5f * Special.Erf((Maths.Log(x) - mu) / Maths.Sqrt(sigma * Maths.Sqrt2)));
}
/// <summary>
/// Gets the cumulative distribution function (cdf) for
/// 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 y = Math.Abs(x);
double den = Math.Sqrt(2) * sigma;
double a = (y + mu) / den;
double b = (y - mu) / den;
double cdf = 0.5 * (Special.Erf(a) + Special.Erf(b));
return(cdf);
}
private double F(double x) // Standard Normal Cumulative Probability Distribution Function
{
if (x > 0)
{
var arg = x / Math.Sqrt(2);
return(0.5 * (1 + Special.Erf(arg)));
}
else
{
var arg = -x / Math.Sqrt(2);
return(0.5 * (1 - Special.Erf(arg)));
}
}
public void InverseErfTest()
{
for (int i = 0; i < 100; i++)
{
double expected = i / 100.0;
double erf = Special.Erf(expected);
double actual = Special.Ierf(erf);
Assert.AreEqual(expected, actual, 1e-15);
Assert.IsFalse(double.IsNaN(expected));
Assert.IsFalse(double.IsNaN(actual));
}
}
/// <summary>
/// von-Mises cumulative distribution function.
/// </summary>
///
/// <remarks>
/// This method implements the Von-Mises CDF calculation code
/// as given by Geoffrey Hill on his original FORTRAN code and
/// shared under the GNU LGPL license.
///
/// <para>
/// References:
/// <list type="bullet">
/// <item><description>Geoffrey Hill, ACM TOMS Algorithm 518,
/// Incomplete Bessel Function I0: The von Mises Distribution,
/// ACM Transactions on Mathematical Software, Volume 3, Number 3,
/// September 1977, pages 279-284.</description></item>
/// </list></para>
/// </remarks>
///
/// <param name="x">The point where to calculate the CDF.</param>
/// <param name="mu">The location parameter μ (mu).</param>
/// <param name="kappa">The concentration parameter κ (kappa).</param>
///
/// <returns>The value of the von-Mises CDF at point <paramref name="x"/>.</returns>
///
public static double DistributionFunction(double x, double mu, double kappa)
{
double a1 = 12.0;
double a2 = 0.8;
double a3 = 8.0;
double a4 = 1.0;
double c1 = 56.0;
double ck = 10.5;
double cdf = 0;
if (x - mu <= -Math.PI)
{
return(0);
}
if (Math.PI <= x - mu)
{
return(1.0);
}
double z = kappa;
double u = (x - mu + Math.PI) % (2.0 * Math.PI);
if (u < 0.0)
{
u = u + 2.0 * Math.PI;
}
double y = u - Math.PI;
if (z <= ck)
{
double v = 0.0;
if (0.0 < z)
{
double ip = Math.Floor(z * a2 - a3 / (z + a4) + a1);
double p = ip;
double s = Math.Sin(y);
double c = Math.Cos(y);
y = p * y;
double sn = Math.Sin(y);
double cn = Math.Cos(y);
double r = 0.0;
z = 2.0 / z;
for (int n = 2; n <= ip; n++)
{
p = p - 1.0;
y = sn;
sn = sn * c - cn * s;
cn = cn * c + y * s;
r = 1.0 / (p * z + r);
v = (sn / p + v) * r;
}
}
cdf = (u * 0.5 + v) / Math.PI;
}
else
{
double c = 24.0 * z;
double v = c - c1;
double r = Math.Sqrt((54.0 / (347.0 / v + 26.0 - c) - 6.0 + c) / 12.0);
z = Math.Sin(0.5 * y) * r;
double s = 2.0 * z * z;
v = v - s + 3.0;
y = (c - s - s - 16.0) / 3.0;
y = ((s + 1.75) * s + 83.5) / v - y;
double arg = z * (1.0 - s / (y * y));
double erfx = Special.Erf(arg);
cdf = 0.5 * erfx + 0.5;
}
cdf = Math.Max(cdf, 0.0);
cdf = Math.Min(cdf, 1.0);
return(cdf);
}
/// <summary>
/// Cumulative distribution function.
/// </summary>
public double CDF(double x)
{
return((1 + Special.Erf(x / Sqrt2)) / 2);
}
public static double[] Laplace(double[] array, double avarage, double disp) // знаходимо функцію лапласа
{
double[] fixedArrayValues = new double[21];
for (int i = 0; i < 21; i++)
{
fixedArrayValues[i] = (array[i] - avarage) / Math.Sqrt(disp);
}
double[] laplaceValues = new double[21];
for (int i = 0; i < 21; i++)
{
laplaceValues[i] = (1 / Math.Sqrt(2 * Math.PI)) * (Math.Sqrt(Math.PI) * (Special.Erf(fixedArrayValues[i] / Math.Sqrt(2)) + 1)) / Math.Sqrt(2);
}
return(laplaceValues);
}
/// <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)
{
return(0.5f + 0.5f * Special.Erf((x - mu) / Maths.Sqrt(2.0f * sigma * sigma)));
}
/// <summary>
/// Normal cumulative distribution function.
/// </summary>
///
/// <returns>
/// The area under the Gaussian p.d.f. integrated
/// from minus infinity to the given value.
/// </returns>
///
public static double Log(double value)
{
return(0.5 * Special.Log1p(Special.Erf(value / Constants.Sqrt2)));
}
/// <summary>
/// Normal cumulative distribution function.
/// </summary>
///
/// <returns>
/// The area under the Gaussian p.d.f. integrated
/// from minus infinity to the given value.
/// </returns>
///
public static double Function(double value)
{
return(0.5 + 0.5 * Special.Erf(value / Constants.Sqrt2));
}