public static double PDFIntegration(double x, double alpha, double precision, ref object tempStorage)
{
if (alpha < 1)
{
GetAlt1GnParameter(x, alpha, out var factorp, out var facdiv, out var dev, out var logPdfPrefactor);
var intg = new Alt1GnI(factorp, facdiv, logPdfPrefactor, alpha, dev);
if (intg.IsMaximumLeftHandSide())
{
return(intg.PDFIntegrate(ref tempStorage, precision));
}
else
{
return(new Alt1GnD(factorp, facdiv, logPdfPrefactor, alpha, dev).Integrate(ref tempStorage, precision));
}
}
else
{
GetAgt1GnParameter(x, alpha, out var factorp, out var factorw, out var dev, out var logPdfPrefactor);
var intg = new Agt1GnI(factorp, factorw, logPdfPrefactor, alpha, dev);
if (intg.IsMaximumLeftHandSide())
{
return(intg.Integrate(ref tempStorage, precision));
}
else
{
return(new Agt1GnD(factorp, factorw, logPdfPrefactor, alpha, dev).Integrate(ref tempStorage, precision));
}
}
}
private static void CDFMethodForPositiveX(double x, double alpha, ref object tempStorage, double precision, out double integFromXZero, out double integFromXInfinity)
{
const double offs = 0.5;
if (alpha < 1)
{
GetAlt1GnParameter(x, alpha, out var factorp, out var facdiv, out var dev, out var logPdfPrefactor);
var inc = new Alt1GnI(factorp, facdiv, logPdfPrefactor, alpha, dev);
if (inc.IsMaximumLeftHandSide())
{
integFromXZero = inc.CDFIntegrate(ref tempStorage, precision) / Math.PI;
integFromXInfinity = offs - integFromXZero;
}
else
{
integFromXInfinity = new Alt1GnD(factorp, facdiv, logPdfPrefactor, alpha, dev).CDFIntegrate(ref tempStorage, precision) / Math.PI;
integFromXZero = offs - integFromXInfinity;
}
}
else if (alpha == 1)
{
if (x <= 1)
{
integFromXZero = Math.Atan(x) / Math.PI;
integFromXInfinity = offs - integFromXZero;
}
else
{
integFromXInfinity = Math.Atan(1 / x) / Math.PI;
integFromXZero = offs - integFromXInfinity;
}
}
else // if(alpha>1)
{
GetAgt1GnParameter(x, alpha, out var factorp, out var factorw, out var dev, out var logPdfPrefactor);
var inc = new Agt1GnI(factorp, factorw, logPdfPrefactor, alpha, dev);
if (inc.IsMaximumLeftHandSide())
{
integFromXInfinity = inc.CDFIntegrate(ref tempStorage, precision) / Math.PI;
integFromXZero = offs - integFromXInfinity;
}
else
{
integFromXZero = new Agt1GnD(factorp, factorw, logPdfPrefactor, alpha, dev).CDFIntegrate(ref tempStorage, precision) / Math.PI;
integFromXInfinity = offs - integFromXZero;
}
}
}
/// <summary>
/// Special case for alpha>1 and gamma near to alpha-2 (i.e. gamma at the negative border).
/// </summary>
/// <param name="x"></param>
/// <param name="alpha"></param>
/// <param name="gamma"></param>
/// <param name="aga"></param>
/// <param name="temp"></param>
/// <param name="precision"></param>
/// <returns></returns>
public static double PDFIntegralAgt1Gn(double x, double alpha, double gamma, double aga, ref object temp, double precision)
{
double factorp, factorw, dev, prefactor;
GetAgt1GnParameterByGamma(x, alpha, gamma, aga, out factorp, out factorw, out dev, out prefactor);
Agt1GnI intI = new Agt1GnI(factorp, factorw, prefactor, alpha, dev);
double integrand;
if (intI.IsMaximumLeftHandSide())
integrand = intI.Integrate(ref temp, precision); // IntegrateFuncExpMFuncInc(delegate(double theta) { return PDFCoreAgt1GnI(factorp, factorw, alpha, dev, theta); }, 0, (Math.PI - dev) / alpha, ref temp, precision);
else
integrand = new Agt1GnD(factorp, factorw, prefactor, alpha, dev).Integrate(ref temp, precision); // IntegrateFuncExpMFuncDec(delegate(double theta) { return PDFCoreAgt1GnD(factorp, factorw, alpha, dev, theta); }, 0, (Math.PI - dev) / alpha, ref temp, precision);
return integrand;
}
private static void CDFMethodForPositiveX(double x, double alpha, ref object tempStorage, double precision, out double integFromXZero, out double integFromXInfinity)
{
const double offs = 0.5;
if (alpha < 1)
{
double factorp, facdiv, dev, logPdfPrefactor;
GetAlt1GnParameter(x, alpha, out factorp, out facdiv, out dev, out logPdfPrefactor);
Alt1GnI inc = new Alt1GnI(factorp, facdiv, logPdfPrefactor, alpha, dev);
if (inc.IsMaximumLeftHandSide())
{
integFromXZero = inc.CDFIntegrate(ref tempStorage, precision) / Math.PI;
integFromXInfinity = offs - integFromXZero;
}
else
{
integFromXInfinity = new Alt1GnD(factorp, facdiv, logPdfPrefactor, alpha, dev).CDFIntegrate(ref tempStorage, precision) / Math.PI;
integFromXZero = offs - integFromXInfinity;
}
}
else if (alpha == 1)
{
if (x <= 1)
{
integFromXZero = Math.Atan(x) / Math.PI;
integFromXInfinity = offs - integFromXZero;
}
else
{
integFromXInfinity = Math.Atan(1 / x) / Math.PI;
integFromXZero = offs - integFromXInfinity;
}
}
else // if(alpha>1)
{
double factorp, factorw, dev, logPdfPrefactor;
GetAgt1GnParameter(x, alpha, out factorp, out factorw, out dev, out logPdfPrefactor);
Agt1GnI inc = new Agt1GnI(factorp, factorw, logPdfPrefactor, alpha, dev);
if (inc.IsMaximumLeftHandSide())
{
integFromXInfinity = inc.CDFIntegrate(ref tempStorage, precision) / Math.PI;
integFromXZero = offs - integFromXInfinity;
}
else
{
integFromXZero = new Agt1GnD(factorp, factorw, logPdfPrefactor, alpha, dev).CDFIntegrate(ref tempStorage, precision) / Math.PI;
integFromXInfinity = offs - integFromXZero;
}
}
}
public static double PDFIntegration(double x, double alpha, double precision, ref object tempStorage)
{
if (alpha < 1)
{
double factorp, facdiv, dev, logPdfPrefactor;
GetAlt1GnParameter(x, alpha, out factorp, out facdiv, out dev, out logPdfPrefactor);
Alt1GnI intg = new Alt1GnI(factorp, facdiv, logPdfPrefactor, alpha, dev);
if (intg.IsMaximumLeftHandSide())
return intg.PDFIntegrate(ref tempStorage, precision);
else
return new Alt1GnD(factorp, facdiv, logPdfPrefactor, alpha, dev).Integrate(ref tempStorage, precision);
}
else
{
double factorp, factorw, dev, logPdfPrefactor;
GetAgt1GnParameter(x, alpha, out factorp, out factorw, out dev, out logPdfPrefactor);
Agt1GnI intg = new Agt1GnI(factorp, factorw, logPdfPrefactor, alpha, dev);
if (intg.IsMaximumLeftHandSide())
return intg.Integrate(ref tempStorage, precision);
else
return new Agt1GnD(factorp, factorw, logPdfPrefactor, alpha, dev).Integrate(ref tempStorage, precision);
}
}