/// <summary>
/// Special case for alpha < 1 and gamma near to +alpha (i.e. gamma at the positive border).
/// Here gamma was set to alpha*(1-dev*2/Pi).
/// </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 PDFIntegralAlt1GpD(double x, double alpha, double gamma, double aga, ref object temp, double precision)
{
double factorp, facdiv, dev, prefactor;
GetAlt1GpParameterByGamma(x, alpha, gamma, aga, out factorp, out facdiv, out dev, out prefactor);
Alt1GpD intD = new Alt1GpD(factorp, facdiv, prefactor, alpha, dev);
double integrand = intD.Integrate(ref temp, precision); // IntegrateFuncExpMFuncDec(delegate(double theta) { return PDFCoreAlt1GpD(factorp, facdiv, alpha, dev, theta); }, 0, dev, ref temp, precision);
return integrand;
}
public static void CDFMethodForPositiveX(double x, double alpha, double gamma, double aga, ref object tempStorage, double precision, out double integFromXZero, out double integFromXInfinity, out double offs)
{
if (alpha <= 0)
throw new ArgumentException("Alpha must be in the range alpha>0");
if (alpha < 1)
{
if (gamma <= 0)
{
offs = 1 - 0.5 * aga;
if (x == 0)
{
integFromXZero = 0;
integFromXInfinity = offs;
}
else // x != 0
{
double factorp, facdiv, dev, logPdfPrefactor;
GetAlt1GnParameterByGamma(x, alpha, gamma, aga, 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 // gamma>0
{
offs = 0.5 * aga;
if (x == 0)
{
integFromXZero = 0;
integFromXInfinity = offs;
}
else // x!=0
{
double factorp, facdiv, dev, logPdfPrefactor;
GetAlt1GpParameterByGamma(x, alpha, gamma, aga, out factorp, out facdiv, out dev, out logPdfPrefactor);
Alt1GpI inc = new Alt1GpI(factorp, facdiv, logPdfPrefactor, alpha, dev);
if (inc.IsMaximumLeftHandSide())
{
integFromXZero = inc.CDFIntegrate(ref tempStorage, precision) / Math.PI;
integFromXInfinity = offs - integFromXZero;
}
else
{
integFromXInfinity = new Alt1GpD(factorp, facdiv, logPdfPrefactor, alpha, dev).CDFIntegrate(ref tempStorage, precision) / Math.PI;
integFromXZero = offs - integFromXInfinity;
}
}
}
}
else if (alpha == 1)
{
double a; // = Math.Cos(gamma*Math.PI/2);
double b; // = Math.Sin(gamma*Math.PI/2);
offs = 0.5;
a = SinXPiBy2(aga); // for alpha=1 aga is 1-gamma or -1+gamma, thus we can turn cosine into sine
b = SinXPiBy2(gamma); // for b it is not important to have high accuracy with gamma=1 or -1
double arg = (b + x) / a;
if (arg <= 1)
{
integFromXZero = Math.Atan(arg) / Math.PI;
integFromXInfinity = offs - integFromXZero;
}
else
{
integFromXInfinity = Math.Atan(1 / arg) / Math.PI;
integFromXZero = offs - integFromXInfinity;
}
}
else if (alpha <= 2)
{
double xinv = Math.Pow(x, -alpha);
double alphainv = 1 / alpha;
double gammainv = (gamma - alpha + 1) / alpha;
double againv = aga;
if (gamma > 0)
againv = gammainv > 0 ? 2 * (alpha - 1) + aga : 2 * (2 - alpha) - aga;
else
againv = aga;
CDFMethodForPositiveX(xinv, alphainv, gammainv, againv, ref tempStorage, precision, out integFromXZero, out integFromXInfinity, out offs);
double h = integFromXZero;
integFromXZero = integFromXInfinity / alpha;
integFromXInfinity = h / alpha;
offs /= alpha;
}
else
{
throw new ArgumentException("Alpha not in the range 0<alpha<=2");
}
}
/// <summary>
/// Special case for alpha < 1 and gamma near to +alpha (i.e. gamma at the positive border).
/// Here gamma was set to alpha*(1-dev*2/Pi).
/// </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 PDFIntegralAlt1Gp(double x, double alpha, double gamma, double aga, ref object temp, double precision)
{
double factorp, facdiv, dev, prefactor;
GetAlt1GpParameterByGamma(x, alpha, gamma, aga, out factorp, out facdiv, out dev, out prefactor);
double integrand;
Alt1GpI intI = new Alt1GpI(factorp, facdiv, prefactor, alpha, dev);
if (intI.IsMaximumLeftHandSide())
integrand = intI.Integrate(ref temp, precision); // IntegrateFuncExpMFuncInc(delegate(double theta) { return PDFCoreAlt1GpI(factorp, facdiv, alpha, dev, theta); }, 0, dev, ref temp, precision);
else
integrand = new Alt1GpD(factorp, facdiv, prefactor, alpha, dev).Integrate(ref temp, precision); // IntegrateFuncExpMFuncDec(delegate(double theta) { return PDFCoreAlt1GpD(factorp, facdiv, alpha, dev, theta); }, 0, dev, ref temp, precision);
return integrand;
}
