/// <summary>
/// Create a truncated Gamma equivalent to a Gamma, i.e. with no truncation.
/// </summary>
/// <param name="Gamma"></param>
public static TruncatedGamma FromGamma(Gamma Gamma)
{
return(new TruncatedGamma(Gamma));
}
/// <summary>
/// Sets this Gamma instance to have the parameter values of that Gamma instance
/// </summary>
/// <param name="that">That Gamma</param>
public void SetTo(Gamma that)
{
Rate = that.Rate;
Shape = that.Shape;
}
/// <summary>
/// Create a truncated Gamma equivalent to a Gamma, i.e. with no truncation.
/// </summary>
/// <param name="that"></param>
public TruncatedGamma(Gamma that)
{
this.Gamma = that;
LowerBound = 0;
UpperBound = Double.PositiveInfinity;
}
/// <summary>
/// Get the derivatives of the log-pdf at a point.
/// </summary>
/// <param name="dist"></param>
/// <param name="x"></param>
/// <param name="dlogp">On exit, the first derivative.</param>
/// <param name="ddlogp">On exit, the second derivative.</param>
public static void GetDerivatives(Gamma dist, double x, out double dlogp, out double ddlogp)
{
dist.GetDerivatives(x, out dlogp, out ddlogp);
}
/// <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>
/// Copy constructor.
/// </summary>
/// <param name="that"></param>
public Gamma(Gamma that)
{
Shape = that.Shape;
Rate = that.Rate;
}
/// <summary>
/// Set the mean and variance to match the moments of a mixture of two Gammas.
/// </summary>
/// <param name="weight1">The first weight</param>
/// <param name="dist1">The first Gamma</param>
/// <param name="weight2">The second weight</param>
/// <param name="dist2">The second Gamma</param>
public void SetToSum(double weight1, Gamma dist1, double weight2, Gamma dist2)
{
SetTo(Gaussian.WeightedSum <Gamma>(this, weight1, dist1, weight2, dist2));
}
/// <summary>
/// Constructs a GammaPower distribution from a Gamma distribution.
/// </summary>
/// <param name="gamma"></param>
/// <param name="power"></param>
/// <returns></returns>
public static GammaPower FromGamma(Gamma gamma, double power)
{
return(FromShapeAndRate(gamma.Shape, gamma.Rate, power));
}