Fixed bug in NormalGamma distribution.

Added documentation to StudentT distribution.

src/Numerics/Distributions/Continuous/StudentT.cs

@@ -39,6 +39,8 @@ namespace MathNet.Numerics.Distributions
     /// <remarks><para>We use a slightly generalized version (compared to Wikipedia) of the Student t-distribution.
     /// Namely, one which also parameterizes the location and scale. See the book "Bayesian Data Analysis" by Gelman
     /// et al. for more details.</para>
+    /// <para>The density of the Student t-distribution 
+    /// p(x|mu,scale,dof) = Gamma((dof+1)/2) (1 + (x - mu)^2 / (scale * scale * dof))^(-(dof+1)/2) / (Gamma(dof/2)*Sqrt(dof*pi*scale)).</para>
     /// <para>The distribution will use the <see cref="System.Random"/> by default. 
     /// Users can get/set the random number generator by using the <see cref="RandomSource"/> property.</para>
     /// <para>The statistics classes will check all the incoming parameters whether they are in the allowed
@@ -232,11 +234,11 @@ namespace MathNet.Numerics.Distributions
             {
                 if (Double.IsPositiveInfinity(_dof))
                 {
-                    return _scale;
+                    return _scale * _scale;
                 }
                 else if (_dof > 2.0)
                 {
-                    return _dof * _scale / (_dof - 2.0);
+                    return _dof * _scale * _scale / (_dof - 2.0);
                 }
                 else if (_dof > 1.0)
                 {
@@ -258,11 +260,11 @@ namespace MathNet.Numerics.Distributions
             {
                 if (Double.IsPositiveInfinity(_dof))
                 {
-                    return Math.Sqrt(_scale);
+                    return Math.Sqrt(_scale * _scale);
                 }
                 else if (_dof > 2.0)
                 {
-                    return Math.Sqrt(_dof * _scale / (_dof - 2.0));
+                    return Math.Sqrt(_dof * _scale * _scale / (_dof - 2.0));
                 }
                 else if (_dof > 1.0)
                 {
@@ -336,7 +338,7 @@ namespace MathNet.Numerics.Distributions
             // TODO JVG we can probably do a better job for Cauchy special case
             if (Double.IsPositiveInfinity(_dof))
             {
-                return Normal.Density(_location, Math.Sqrt(_scale), x);
+                return Normal.Density(_location, _scale, x);
             }
             else
             {
@@ -359,7 +361,7 @@ namespace MathNet.Numerics.Distributions
             // TODO JVG we can probably do a better job for Cauchy special case
             if (Double.IsPositiveInfinity(_dof))
             {
-                return Normal.DensityLn(_location, Math.Sqrt(_scale), x);
+                return Normal.DensityLn(_location, _scale, x);
             }
             else
             {

src/Numerics/Distributions/Multivariate/NormalGamma.cs

@@ -242,11 +242,11 @@ namespace MathNet.Numerics.Distributions
         {
             if (Double.IsPositiveInfinity(_precisionInvScale))
             {
-                return new StudentT(_meanLocation, _meanScale * _precisionShape, Double.PositiveInfinity);
+                return new StudentT(_meanLocation, 1.0 / (_meanScale * _precisionShape), Double.PositiveInfinity);
             }
             else
             {
-                return new StudentT(_meanLocation, _meanScale * _precisionShape / _precisionInvScale, 2.0 * _precisionShape);
+                return new StudentT(_meanLocation, Math.Sqrt(_precisionInvScale / (_meanScale * _precisionShape)), 2.0 * _precisionShape);
             }
         }
 

src/UnitTests/DistributionTests/Continuous/StudentTTests.cs

@@ -172,8 +172,8 @@ namespace MathNet.Numerics.UnitTests.DistributionTests
         [Row(0.0, 1.0, 3.0, 3.0)]
         [Row(0.0, 10.0, 1.0, Double.NaN)]
         [Row(0.0, 10.0, 2.0, Double.PositiveInfinity)]
-        [Row(0.0, 10.0, 2.5, 50.0)]
+        [Row(0.0, 10.0, 2.5, 500.0)]
-        [Row(0.0, 10.0, Double.PositiveInfinity, 10.0)]
+        [Row(0.0, 10.0, Double.PositiveInfinity, 100.0)]
         [Row(10.0, 1.0, 1.0, Double.NaN)]
         [Row(10.0, 1.0, 2.5, 5.0)]
         [Row(-5.0, 100.0, 1.5, Double.PositiveInfinity)]
@@ -190,8 +190,8 @@ namespace MathNet.Numerics.UnitTests.DistributionTests
         [Row(0.0, 1.0, 3.0, 1.7320508075688772935274463415059)]
         [Row(0.0, 10.0, 1.0, Double.NaN)]
         [Row(0.0, 10.0, 2.0, Double.PositiveInfinity)]
-        [Row(0.0, 10.0, 2.5, 7.0710678118654752440084436210485)]
+        [Row(0.0, 10.0, 2.5, 22.360679774997896964091736687313)]
-        [Row(0.0, 10.0, Double.PositiveInfinity, 3.1622776601683793319988935444327)]
+        [Row(0.0, 10.0, Double.PositiveInfinity, 10.0)]
         [Row(10.0, 1.0, 1.0, Double.NaN)]
         [Row(10.0, 1.0, 2.5, 2.2360679774997896964091736687313)]
         [Row(-5.0, 100.0, 1.5, Double.PositiveInfinity)]

src/UnitTests/DistributionTests/Multivariate/NormalGammaTests.cs

@@ -153,7 +153,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests
         [Test, MultipleAsserts]
         [Row(0.0, 1.0, 1.0, 1.0, 0.0, 1.0, 2.0)]
         [Row(10.0, 1.0, 2.0, 2.0, 10.0, 1.0, 4.0)]
-        [Row(10.0, 1.0, 2.0, Double.PositiveInfinity, 10.0, 2.0, Double.PositiveInfinity)]
+        [Row(10.0, 1.0, 2.0, Double.PositiveInfinity, 10.0, 0.5, Double.PositiveInfinity)]
         public void CanGetMeanMarginal(double meanLocation, double meanScale, double precShape, double precInvScale,
             double meanMarginalMean, double meanMarginalScale, double meanMarginalDoF)
         {
@@ -209,7 +209,8 @@ namespace MathNet.Numerics.UnitTests.DistributionTests
         public void SampleFollowsCorrectDistribution()
         {
             Random rnd = new MersenneTwister();
-            var cd = new NormalGamma(1.0, 4.0, 3.0, 3.5);
+            //var cd = new NormalGamma(1.0, 4.0, 3.0, 3.5);
+            var cd = new NormalGamma(1.0, 4.0, 7.0, 3.5);
 
             // Sample from the distribution.
             MeanPrecisionPair[] samples = new MeanPrecisionPair[CommonDistributionTests.NumberOfTestSamples];