/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="PlusGammaOp"]/message_doc[@name="SumAverageConditional(GammaPower, double)"]/*'/> public static GammaPower SumAverageConditional([SkipIfUniform] GammaPower a, double b) { if (double.IsInfinity(b) || double.IsNaN(b)) { throw new ArgumentOutOfRangeException(nameof(b), b, $"Argument is outside the range of supported values."); } if (a.IsUniform() || b == 0) { return(a); } else if (a.Power == 0) { throw new ArgumentException($"Cannot add {b} to {a}"); } else if (a.IsPointMass) { return(GammaPower.PointMass(a.Point + b, a.Power)); } else if (a.Power < 0) { if (a.Shape <= a.Power) { return(a); // mode is at zero } // The mode is ((Shape - Power)/Rate)^Power // We want to shift the mode by b, preserving the Shape and Power. // This implies ((Shape - Power)/newRate)^Power = newMode // newRate = (Shape - Power)/newMode^(1/Power) // = (a.Shape - a.Power) * Math.Pow(a.GetMode() + b, -1 / a.Power); //double logMode = a.Power * (Math.Log(Math.Max(0, a.Shape - a.Power)) - Math.Log(a.Rate)); //if (logMode > double.MaxValue) return a; // mode is at infinity double logShapeMinusPower = Math.Log(a.Shape - a.Power); double mode = a.GetMode(); if (mode > double.MaxValue) { return(a); // mode is at infinity } double newMode = Math.Max(0, mode + b); double newLogMode = Math.Log(newMode); // Find newLogRate to satisfy a.Power*(logShapeMinusPower - newLogRate) <= newLogMode // logShapeMinusPower - newLogRate >= newLogMode/a.Power // newLogRate - logShapeMinusPower <= -newLogMode/a.Power double newLogModeOverPower = MMath.LargestDoubleRatio(newLogMode, -a.Power); double newLogRate = MMath.LargestDoubleSum(logShapeMinusPower, newLogModeOverPower); if ((double)((logShapeMinusPower - newLogRate) * a.Power) > newLogMode) { throw new Exception(); } // Ideally this would find largest newRate such that log(newRate) <= newLogRate double newRate = Math.Exp(newLogRate); if (logShapeMinusPower == newLogRate) { newRate = a.Shape - a.Power; } if (a.Rate > 0) { newRate = Math.Max(double.Epsilon, newRate); } if (!double.IsPositiveInfinity(a.Rate)) { newRate = Math.Min(double.MaxValue, newRate); } return(GammaPower.FromShapeAndRate(a.Shape, newRate, a.Power)); } else if (!a.IsProper()) { return(a); } else { // The mean is Math.Exp(Power * (MMath.RisingFactorialLnOverN(Shape, Power) - Math.Log(Rate))) // We want to shift the mean by b, preserving the Shape and Power. // This implies log(newRate) = MMath.RisingFactorialLnOverN(Shape, Power) - log(newMean)/Power double logShape = MMath.RisingFactorialLnOverN(a.Shape, a.Power); //double logMean = a.GetLogMeanPower(1); //double newLogMean = (b > 0) ? // MMath.LogSumExp(logMean, Math.Log(b)) : // MMath.LogDifferenceOfExp(logMean, Math.Log(-b)); double newMean = Math.Max(0, a.GetMean() + b); double newLogMean = Math.Log(newMean); // If logShape is big, this difference can lose accuracy // Find newLogRate to satisfy logShape - newLogRate <= newLogMean/a.Power double newLogMeanOverPower = MMath.LargestDoubleRatio(newLogMean, a.Power); double newLogRate = -MMath.LargestDoubleSum(-logShape, newLogMeanOverPower); // check: (logShape - newLogRate)*a.Power <= newLogMean if ((double)((logShape - newLogRate) * a.Power) > newLogMean) { throw new Exception(); } double newRate = Math.Exp(newLogRate); newRate = Math.Max(double.Epsilon, newRate); if (!double.IsPositiveInfinity(a.Rate)) { newRate = Math.Min(double.MaxValue, newRate); } return(GammaPower.FromShapeAndRate(a.Shape, newRate, a.Power)); } }