private static double GetGaussianQuantile(double probability, double x0, double p0, double x1, double p1)
{
double mean, stddev;
GetGaussianFromQuantiles(x0, p0, x1, p1, out mean, out stddev);
return(MMath.NormalCdfInv(probability) * stddev + mean);
}
/// <summary>
/// Returns the value x such that GetProbLessThan(x) == probability.
/// </summary>
/// <param name="probability">A real number in [0,1].</param>
/// <returns></returns>
public double GetQuantile(double probability)
{
if (probability < 0)
{
throw new ArgumentOutOfRangeException("probability < 0");
}
if (probability > 1)
{
throw new ArgumentOutOfRangeException("probability > 1");
}
if (this.IsPointMass)
{
return((probability == 1.0) ? MMath.NextDouble(this.Point) : this.Point);
}
else if (Precision <= 0.0)
{
throw new ImproperDistributionException(this);
}
else
{
double mean = MeanTimesPrecision / Precision;
double sqrtPrec = Math.Sqrt(Precision);
return(MMath.NormalCdfInv(probability) / sqrtPrec + mean);
}
}
public static int Histogramize(double value, double mean, double deviation, int numberOfBins)
{
for (int ii = 1; ii <= numberOfBins; ii++)
{
double above = MMath.NormalCdfInv(((double)ii) / ((double)numberOfBins));
if (((value - mean) / deviation) < above)
{
return(ii - 1);
}
}
return(numberOfBins - 1);
}
private static void GetGaussianFromQuantiles(double x0, double p0, double x1, double p1, out double mean, out double deviation)
{
double z0 = MMath.NormalCdfInv(p0);
double z1 = MMath.NormalCdfInv(p1);
// solve for the equivalent Gaussian mean and stddev
Matrix Z = new Matrix(new double[, ] {
{ 1, z0 }, { 1, z1 }
});
DenseVector X = DenseVector.FromArray(x0, x1);
DenseVector A = DenseVector.Zero(2);
A.SetToLeastSquares(X, Z);
mean = A[0];
deviation = A[1];
}
/// <summary>
/// Returns the value x such that GetProbLessThan(x) == probability.
/// </summary>
/// <param name="probability">A real number in [0,1].</param>
/// <returns></returns>
public double GetQuantile(double probability)
{
if (this.IsPointMass)
{
return((probability == 1.0) ? (this.Point + MMath.Ulp(this.Point)) : this.Point);
}
else if (Precision <= 0.0)
{
throw new ImproperDistributionException(this);
}
else
{
double mean = MeanTimesPrecision / Precision;
double sqrtPrec = Math.Sqrt(Precision);
return(MMath.NormalCdfInv(probability) / sqrtPrec + mean);
}
}