/// <summary>
/// Construct a Gamma distribution whose pdf has the given derivatives at a point.
/// </summary>
/// <param name="x">Must be positive</param>
/// <param name="dLogP">Desired derivative of log-density at x</param>
/// <param name="ddLogP">Desired second derivative of log-density at x</param>
/// <param name="forceProper">If true and both derivatives cannot be matched by a proper distribution, match only the first.</param>
/// <returns></returns>
public static Gamma FromDerivatives(double x, double dLogP, double ddLogP, bool forceProper)
{
if (x <= 0)
{
throw new ArgumentException("x <= 0");
}
double a = -x * x * ddLogP;
if (ddLogP == 0.0)
{
a = 0.0; // in case x is infinity
}
if (forceProper)
{
if (dLogP < 0)
{
if (a < 0)
{
a = 0;
}
}
else
{
double amin = x * dLogP;
if (a < amin)
{
a = amin;
}
}
}
double b = a / x - dLogP;
if (forceProper)
{
// correct roundoff errors that might make b negative
b = Math.Max(b, 0);
}
return(Gamma.FromShapeAndRate(a + 1, b));
}
/// <summary>
/// Construct a Gamma distribution whose pdf has the given derivatives at a point.
/// </summary>
/// <param name="x">Cannot be negative</param>
/// <param name="dLogP">Desired derivative of log-density at x</param>
/// <param name="ddLogP">Desired second derivative of log-density at x</param>
/// <param name="forceProper">If true and both derivatives cannot be matched by a proper distribution, match only the first.</param>
/// <returns></returns>
public static Gamma FromDerivatives(double x, double dLogP, double ddLogP, bool forceProper)
{
if (x < 0)
{
throw new ArgumentOutOfRangeException(nameof(x), x, "x < 0");
}
double a;
if (double.IsPositiveInfinity(x))
{
if (ddLogP < 0)
{
return(Gamma.PointMass(x));
}
else if (ddLogP == 0)
{
a = 0.0;
}
else if (forceProper)
{
if (dLogP <= 0)
{
return(Gamma.FromShapeAndRate(1, -dLogP));
}
else
{
return(Gamma.PointMass(x));
}
}
else
{
return(Gamma.FromShapeAndRate(-x, -x - dLogP));
}
}
else
{
a = -x * x * ddLogP;
if (a + 1 > double.MaxValue)
{
return(Gamma.PointMass(x));
}
}
if (forceProper)
{
if (dLogP <= 0)
{
if (a < 0)
{
a = 0;
}
}
else
{
double amin = x * dLogP;
if (a < amin)
{
return(Gamma.FromShapeAndRate(amin + 1, 0));
}
}
}
double b = ((a == 0) ? 0 : (a / x)) - dLogP;
if (forceProper)
{
// correct roundoff errors that might make b negative
b = Math.Max(b, 0);
}
return(Gamma.FromShapeAndRate(a + 1, b));
}
/// <summary>
/// Adds a GammaPower distribution item to the estimator
/// </summary>
/// <param name="distribution">The distribution instance to add</param>
/// <param name="weight">The weight of the sample</param>
public void Add(GammaPower distribution, double weight)
{
gammaEstimator.Add(Gamma.FromShapeAndRate(distribution.Shape, distribution.Rate), weight);
}