public GPDApproximation(IList <double> data, FittingMethod method = FittingMethod.Pickands_SupNorm, Random rand = null)
{
if (data.Count < 30)
{
throw new ArgumentException("Insufficient data count for Pickands Balkema De Haan theorem.");
}
sortedData = new List <double>(data);
sortedData.Sort();
int m; // Transition index
switch (method)
{
case FittingMethod.BFGS_MSE:
ApproximateExcessDistributionParametersBFGS(sortedData, out a, out c, out transitionAbscissa);
// Compute the index of the closest element that is at or before u in the data
int transitionIndex = sortedData.BinarySearch(transitionAbscissa);
if (transitionIndex < 0)
{
transitionIndex = ~transitionIndex;
}
transitionProportion = transitionIndex * 1.0 / sortedData.Count; // Shouldn't this be + 1 here?
break;
case FittingMethod.Moments_MSE:
ApproximateExcessDistributionParametersMoments(sortedData, out a, out c, out m);
transitionProportion = (sortedData.Count - m + 1.0) / sortedData.Count;
transitionAbscissa = sortedData[sortedData.Count - m]; // Convert from m to the actual transitionIndex; m is guaranteed to be > 0
break;
case FittingMethod.V4:
ApproximateExcessDistributionParametersV4(sortedData, out a, out c, out transitionAbscissa);
int transitionIdx = sortedData.BinarySearch(transitionAbscissa);
if (transitionIdx < 0)
{
transitionIdx = ~transitionIdx; // Now the index of the next-largest element
if (transitionIdx == 0)
{
transitionProportion = 0; break;
}
transitionProportion = Interpolation.Lerp(
sortedData[transitionIdx - 1], transitionIdx * 1.0 / sortedData.Count,
sortedData[transitionIdx], (transitionIdx + 1) * 1.0 / sortedData.Count,
transitionAbscissa);
break;
}
transitionProportion = (transitionIdx + 1) * 1.0 / sortedData.Count;
break;
default:
ApproximateExcessDistributionParametersPickands(sortedData, out a, out c, out m); // Write m to transitionIndex
transitionProportion = (sortedData.Count - 4 * m + 1.0) / sortedData.Count;
transitionAbscissa = sortedData[sortedData.Count - 4 * m]; // Convert from m to the actual transitionIndex; m is guaranteed to be > 0
break;
}
this.rand = rand ?? Program.rand;
}
public static double Quantile(IList <double> sortedData, double q)
{
if (q < 0 || q > 1)
{
throw new ArgumentOutOfRangeException($"Desired percentile is out of range: {q}");
}
if (q == 0)
{
return(sortedData[0]);
}
if (q == 1)
{
return(sortedData[sortedData.Count - 1]);
}
double product = (sortedData.Count - 1) * q;
int idx = (int)product;
//return data[idx + 1] * (product - idx) + data[idx] * (idx + 1 - product);
return(Interpolation.Lerp(idx, sortedData[idx], idx + 1, sortedData[idx + 1], product));
}
/// <summary>
/// Returns the value of the quantile function for this distribution at a given quantile
/// </summary>
public double Quantile(double q)
{
// Edge cases
if (q < cumulativeDensities[0])
{
return(abscissas[0]);
}
if (q > cumulativeDensities[cumulativeDensities.Count - 1])
{
return(abscissas[abscissas.Count - 1]);
}
// Fast search for which elements to interpolate between
int idx = cumulativeDensities.BinarySearch(q);
// If q is an element of the cumulative densities list, return the corresponding abscissa
if (idx > -1)
{
return(abscissas[idx]);
}
// Interpolate
idx = ~idx; // idx is now the index of the next largest element of cumulative densities from q
return(Interpolation.Lerp(cumulativeDensities[idx - 1], abscissas[idx - 1], cumulativeDensities[idx], abscissas[idx], q));
}
/// <summary>
/// Returns the value of this distribution's CDF at the given location
/// </summary>
public double CumulativeDensity(double x)
{
// Edge cases
if (x < abscissas[0])
{
return(0);
}
if (x > abscissas[abscissas.Count - 1])
{
return(1);
}
// Fast search for which elements to interpolate between
int idx = abscissas.BinarySearch(x);
// If x is an element of the abscissas, return the corresponding value
if (idx > -1)
{
return(cumulativeDensities[idx]);
}
// Interpolate
idx = ~idx; // idx is now the index of the next largest element of abscissas from x
return(Interpolation.Lerp(abscissas[idx - 1], cumulativeDensities[idx - 1], abscissas[idx], cumulativeDensities[idx], x));
}