|
|
|
@ -48,7 +48,7 @@ namespace MathNet.Numerics.Distributions |
|
|
|
/// <a href="">https://cran.r-project.org/web/packages/sgt/vignettes/sgt.pdf</a>. Compared to that
|
|
|
|
/// implementation, the options for mean adjustment and variance adjustment are always true.
|
|
|
|
/// The location (μ) is the mean of the distribution.
|
|
|
|
/// The scale (σ) squared is the variance of the distribution.
|
|
|
|
/// The scale (σ) squared is the variance of the distribution.
|
|
|
|
/// </para>
|
|
|
|
/// <para>The distribution will use the <see cref="System.Random"/> by
|
|
|
|
/// default. Users can get/set the random number generator by using the
|
|
|
|
@ -57,14 +57,14 @@ namespace MathNet.Numerics.Distributions |
|
|
|
/// whether they are in the allowed range.</para></remarks>
|
|
|
|
public class SkewedGeneralizedT : IContinuousDistribution |
|
|
|
{ |
|
|
|
private System.Random _random; |
|
|
|
System.Random _random; |
|
|
|
|
|
|
|
// If the given parameterization is one of the recognized special cases, then
|
|
|
|
// this variable is non-null and the special case is used for all functions.
|
|
|
|
// Else this value is null and the full formulation of the generalized distribution is used.
|
|
|
|
private IContinuousDistribution _d; |
|
|
|
IContinuousDistribution _d; |
|
|
|
|
|
|
|
private readonly double _skewness; |
|
|
|
readonly double _skewness; |
|
|
|
|
|
|
|
/// <summary>
|
|
|
|
/// Initializes a new instance of the SkewedGeneralizedT class. This is a skewed generalized t-distribution
|
|
|
|
@ -108,7 +108,9 @@ namespace MathNet.Numerics.Distributions |
|
|
|
_d = FindSpecializedDistribution(location, scale, skew, p, q); |
|
|
|
|
|
|
|
if (_d == null) |
|
|
|
{ |
|
|
|
_skewness = CalculateSkewness(); |
|
|
|
} |
|
|
|
} |
|
|
|
|
|
|
|
/// <summary>
|
|
|
|
@ -139,8 +141,8 @@ namespace MathNet.Numerics.Distributions |
|
|
|
/// </summary>
|
|
|
|
public System.Random RandomSource |
|
|
|
{ |
|
|
|
get { return _random; } |
|
|
|
set { _random = value ?? SystemRandomSource.Default; } |
|
|
|
get => _random; |
|
|
|
set => _random = value ?? SystemRandomSource.Default; |
|
|
|
} |
|
|
|
|
|
|
|
/// <summary>
|
|
|
|
@ -149,7 +151,7 @@ namespace MathNet.Numerics.Distributions |
|
|
|
/// <returns>a string representation of the distribution.</returns>
|
|
|
|
public override string ToString() |
|
|
|
{ |
|
|
|
return $"SkewedGeneralizedT(μ = {Location}, σ = {Scale}, λ = { Skew }, p = {P}, q = {Q})"; |
|
|
|
return $"SkewedGeneralizedT(μ = {Location}, σ = {Scale}, λ = {Skew}, p = {P}, q = {Q})"; |
|
|
|
} |
|
|
|
|
|
|
|
/// <summary>
|
|
|
|
@ -168,61 +170,57 @@ namespace MathNet.Numerics.Distributions |
|
|
|
/// <summary>
|
|
|
|
/// Gets the location (μ) of the Skewed Generalized t-distribution.
|
|
|
|
/// </summary>
|
|
|
|
public double Location { get; private set; } |
|
|
|
public double Location { get; } |
|
|
|
|
|
|
|
/// <summary>
|
|
|
|
/// Gets the scale (σ) of the Skewed Generalized t-distribution. Range: σ > 0.
|
|
|
|
/// </summary>
|
|
|
|
public double Scale { get; private set; } |
|
|
|
public double Scale { get; } |
|
|
|
|
|
|
|
/// <summary>
|
|
|
|
/// Gets the skew (λ) of the Skewed Generalized t-distribution. Range: 1 > λ > -1.
|
|
|
|
/// </summary>
|
|
|
|
public double Skew { get; private set; } |
|
|
|
public double Skew { get; } |
|
|
|
|
|
|
|
/// <summary>
|
|
|
|
/// Gets the first parameter that controls the kurtosis of the distribution. Range: p > 0.
|
|
|
|
/// </summary>
|
|
|
|
public double P { get; private set; } |
|
|
|
public double P { get; } |
|
|
|
|
|
|
|
/// <summary>
|
|
|
|
/// Gets the second parameter that controls the kurtosis of the distribution. Range: q > 0.
|
|
|
|
/// </summary>
|
|
|
|
public double Q { get; private set; } |
|
|
|
public double Q { get; } |
|
|
|
|
|
|
|
// No skew implies Median=Mode=Mean
|
|
|
|
public double Mode => _d == null ? |
|
|
|
Skew == 0 ? Mean : Mean - AdjustAddend(AdjustScale(Scale, Skew, P, Q), Skew, P, Q) : |
|
|
|
_d.Mode; |
|
|
|
public double Mode => _d?.Mode ?? (Skew == 0 ? Mean : Mean - AdjustAddend(AdjustScale(Scale, Skew, P, Q), Skew, P, Q)); |
|
|
|
|
|
|
|
public double Minimum => _d == null ? double.NegativeInfinity : _d.Minimum; |
|
|
|
public double Minimum => _d?.Minimum ?? double.NegativeInfinity; |
|
|
|
|
|
|
|
public double Maximum => _d == null ? double.PositiveInfinity : _d.Maximum; |
|
|
|
public double Maximum => _d?.Maximum ?? double.PositiveInfinity; |
|
|
|
|
|
|
|
// Mean=Location due to our adjustments made
|
|
|
|
public double Mean => _d == null ? Location : _d.Mean; |
|
|
|
public double Mean => _d?.Mean ?? Location; |
|
|
|
|
|
|
|
// Variance=Scale*Scale due to our adjustments made
|
|
|
|
public double Variance => _d == null ? Scale * Scale : _d.Variance; |
|
|
|
public double Variance => _d?.Variance ?? Scale * Scale; |
|
|
|
|
|
|
|
public double StdDev => _d == null ? Scale : _d.StdDev; |
|
|
|
public double StdDev => _d?.StdDev ?? Scale; |
|
|
|
|
|
|
|
public double Entropy => _d == null ? throw new NotImplementedException() : _d.Entropy; |
|
|
|
public double Entropy => _d?.Entropy ?? throw new NotImplementedException(); |
|
|
|
|
|
|
|
public double Skewness => _d == null ? |
|
|
|
_skewness : |
|
|
|
_d.Skewness; |
|
|
|
public double Skewness => _d?.Skewness ?? _skewness; |
|
|
|
|
|
|
|
// No skew implies Median=Mode=Mean
|
|
|
|
// Else find it via the point where CDF gives 0.5
|
|
|
|
public double Median => _d == null ? |
|
|
|
Skew == 0 ? Mean : InverseCumulativeDistribution(0.5) : |
|
|
|
_d.Median; |
|
|
|
public double Median => _d?.Median ?? (Skew == 0 ? Mean : InverseCumulativeDistribution(0.5)); |
|
|
|
|
|
|
|
private double CalculateSkewness() |
|
|
|
double CalculateSkewness() |
|
|
|
{ |
|
|
|
if (P * Q <= 3 || Skew == 0) |
|
|
|
{ |
|
|
|
return 0.0; |
|
|
|
} |
|
|
|
|
|
|
|
var scale = AdjustScale(Scale, Skew, P, Q); |
|
|
|
var b1 = SpecialFunctions.Beta(1.0 / P, Q); |
|
|
|
@ -239,7 +237,7 @@ namespace MathNet.Numerics.Distributions |
|
|
|
return t1 * (t2 - t3 * t4 + t5); |
|
|
|
} |
|
|
|
|
|
|
|
private static double AdjustScale(double scale, double skew, double p, double q) |
|
|
|
static double AdjustScale(double scale, double skew, double p, double q) |
|
|
|
{ |
|
|
|
var b1 = SpecialFunctions.Beta(3.0 / p, q - 2.0 / p); |
|
|
|
var b2 = SpecialFunctions.Beta(1.0 / p, q); |
|
|
|
@ -250,13 +248,13 @@ namespace MathNet.Numerics.Distributions |
|
|
|
} |
|
|
|
|
|
|
|
// Note: Scale is assumed to be adjusted already when calling this function.
|
|
|
|
private static double AdjustX(double x, double scale, double skew, double p, double q) |
|
|
|
static double AdjustX(double x, double scale, double skew, double p, double q) |
|
|
|
{ |
|
|
|
return x + AdjustAddend(scale, skew, p, q); |
|
|
|
} |
|
|
|
|
|
|
|
// Note: Scale is assumed to be adjusted already when calling this function.
|
|
|
|
private static double AdjustAddend(double scale, double skew, double p, double q) |
|
|
|
static double AdjustAddend(double scale, double skew, double p, double q) |
|
|
|
{ |
|
|
|
var b1 = SpecialFunctions.Beta(2.0 / p, q - 1.0 / p); |
|
|
|
var b2 = SpecialFunctions.Beta(1.0 / p, q); |
|
|
|
@ -308,7 +306,7 @@ namespace MathNet.Numerics.Distributions |
|
|
|
return fn(x); |
|
|
|
} |
|
|
|
|
|
|
|
private static double PDFull(double location, double scale, double skew, double p, double q, double x) |
|
|
|
static double PDFull(double location, double scale, double skew, double p, double q, double x) |
|
|
|
{ |
|
|
|
scale = AdjustScale(scale, skew, p, q); |
|
|
|
x = AdjustX(x, scale, skew, p, q); |
|
|
|
@ -322,7 +320,7 @@ namespace MathNet.Numerics.Distributions |
|
|
|
return p / denominator; |
|
|
|
} |
|
|
|
|
|
|
|
private static double PDFullLn(double location, double scale, double skew, double p, double q, double x) |
|
|
|
static double PDFullLn(double location, double scale, double skew, double p, double q, double x) |
|
|
|
{ |
|
|
|
scale = AdjustScale(scale, skew, p, q); |
|
|
|
x = AdjustX(x, scale, skew, p, q); |
|
|
|
@ -337,7 +335,7 @@ namespace MathNet.Numerics.Distributions |
|
|
|
// by Hansen, McDonald and Newey (2010).
|
|
|
|
// Note that, for all cases where skew is required to be 0, if skew is non-zero, this
|
|
|
|
// simply gives the corresponding skewed version of the distribution.
|
|
|
|
private static Func<double, double> PDFunc(double location, double scale, double skew, double p, double q, bool ln) |
|
|
|
static Func<double, double> PDFunc(double location, double scale, double skew, double p, double q, bool ln) |
|
|
|
{ |
|
|
|
if (p == double.PositiveInfinity) |
|
|
|
{ |
|
|
|
@ -414,10 +412,13 @@ namespace MathNet.Numerics.Distributions |
|
|
|
// InverseCumulativeDistribution is not a part of the interface, so resort to type-checking.
|
|
|
|
if (d != null) |
|
|
|
{ |
|
|
|
if (d is SkewedGeneralizedError sge) |
|
|
|
return sge.InverseCumulativeDistribution(pr); |
|
|
|
if (d is ContinuousUniform u) |
|
|
|
return u.InverseCumulativeDistribution(pr); |
|
|
|
switch (d) |
|
|
|
{ |
|
|
|
case SkewedGeneralizedError sge: |
|
|
|
return sge.InverseCumulativeDistribution(pr); |
|
|
|
case ContinuousUniform u: |
|
|
|
return u.InverseCumulativeDistribution(pr); |
|
|
|
} |
|
|
|
} |
|
|
|
|
|
|
|
// Note: Adapted from the R package,
|
|
|
|
@ -444,7 +445,7 @@ namespace MathNet.Numerics.Distributions |
|
|
|
|
|
|
|
public double CumulativeDistribution(double x) |
|
|
|
{ |
|
|
|
return _d == null ? CDF(Location, Scale, Skew, P, Q, x) : _d.CumulativeDistribution(x); |
|
|
|
return _d?.CumulativeDistribution(x) ?? CDF(Location, Scale, Skew, P, Q, x); |
|
|
|
} |
|
|
|
|
|
|
|
/// <summary>
|
|
|
|
@ -459,10 +460,13 @@ namespace MathNet.Numerics.Distributions |
|
|
|
// InverseCumulativeDistribution is not a part of the interface, so resort to type-checking.
|
|
|
|
if (_d != null) |
|
|
|
{ |
|
|
|
if (_d is SkewedGeneralizedError sge) |
|
|
|
return sge.InverseCumulativeDistribution(p); |
|
|
|
if (_d is ContinuousUniform u) |
|
|
|
return u.InverseCumulativeDistribution(p); |
|
|
|
switch (_d) |
|
|
|
{ |
|
|
|
case SkewedGeneralizedError sge: |
|
|
|
return sge.InverseCumulativeDistribution(p); |
|
|
|
case ContinuousUniform u: |
|
|
|
return u.InverseCumulativeDistribution(p); |
|
|
|
} |
|
|
|
} |
|
|
|
|
|
|
|
return InvCDF(Location, Scale, Skew, P, Q, p); |
|
|
|
@ -470,12 +474,12 @@ namespace MathNet.Numerics.Distributions |
|
|
|
|
|
|
|
public double Density(double x) |
|
|
|
{ |
|
|
|
return _d == null ? PDF(Location, Scale, Skew, P, Q, x) : _d.Density(x); |
|
|
|
return _d?.Density(x) ?? PDF(Location, Scale, Skew, P, Q, x); |
|
|
|
} |
|
|
|
|
|
|
|
public double DensityLn(double x) |
|
|
|
{ |
|
|
|
return _d == null ? PDFLn(Location, Scale, Skew, P, Q, x) : _d.DensityLn(x); |
|
|
|
return _d?.DensityLn(x) ?? PDFLn(Location, Scale, Skew, P, Q, x); |
|
|
|
} |
|
|
|
|
|
|
|
/// <summary>
|
|
|
|
@ -541,7 +545,7 @@ namespace MathNet.Numerics.Distributions |
|
|
|
return SampleUnchecked(SystemRandomSource.Default, location, scale, skew, p, q); |
|
|
|
} |
|
|
|
|
|
|
|
private static double SampleUnchecked(System.Random rnd, double location, double scale, double skew, double p, double q) |
|
|
|
static double SampleUnchecked(System.Random rnd, double location, double scale, double skew, double p, double q) |
|
|
|
{ |
|
|
|
var u = ContinuousUniform.Sample(rnd, 0, 1); |
|
|
|
return InvCDF(location, scale, skew, p, q, u); |
|
|
|
|
Christoph Ruegg
6 years ago