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;
                }
            }
        }
		private static double CDFIntegralForPositiveXAgt1(double x, double alpha, double gamma, double aga, ref object temp, double precision)
		{
			double factorp, factorw, dev, logPdfPrefactor;
			GetAgt1GnParameterByGamma(x, alpha, gamma, aga, out factorp, out factorw, out dev, out logPdfPrefactor);
			Agt1GnI a = new Agt1GnI(factorp, factorw, logPdfPrefactor, alpha, dev);
			return a.CDFIntegrate(ref temp, precision);
		}
		/// <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 PDFIntegralAgt1GnI(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 = intI.Integrate(ref temp, precision); // IntegrateFuncExpMFuncInc(delegate(double theta) { return PDFCoreAgt1GnI(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);
			}
		}