Distributions: discrete distribution Median should be double; multiple modes #189 #187

src/Numerics/Distributions/Bernoulli.cs

@@ -176,12 +176,20 @@ namespace MathNet.Numerics.Distributions
             get { return _p > 0.5 ? 1 : 0; }
         }
 
+        /// <summary>
+        /// Gets all modes of the distribution.
+        /// </summary>
+        public int[] Modes
+        {
+            get { return _p < 0.5 ? new[] { 0 } : P > 0.5 ? new[] { 1 } : new[] { 0, 1 }; }
+        }
+
         /// <summary>
         /// Gets the median of the distribution.
         /// </summary>
-        public int Median
+        public double Median
         {
-            get { throw new NotSupportedException("The median of the Bernoulli distribution is undefined."); }
+            get { return _p < 0.5 ? 0.0 : _p > 0.5 ? 1.0 : 0.5; }
         }
 
         /// <summary>

src/Numerics/Distributions/Binomial.cs

@@ -213,12 +213,28 @@ namespace MathNet.Numerics.Distributions
             }
         }
 
+        /// <summary>
+        /// Gets all modes of the distribution.
+        /// </summary>
+        public int[] Modes
+        {
+            get
+            {
+                if (_p == 1.0) return new [] {_trials};
+                if (_p == 0.0) return new [] {0};
+
+                double td = (_trials + 1)*_p;
+                int t = (int)Math.Floor(td);
+                return t != td ? new[] { t } : new[] { t, t - 1 };
+            }
+        }
+
         /// <summary>
         /// Gets the median of the distribution.
         /// </summary>
-        public int Median
+        public double Median
         {
-            get { return (int)Math.Floor(_p*_trials); }
+            get { return Math.Floor(_p*_trials); }
         }
 
         /// <summary>
@@ -371,7 +387,6 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Samples a binomially distributed random variable.
         /// </summary>
-        /// <param name="rnd">The random number generator to use.</param>
         /// <param name="p">The success probability (p) in each trial. Range: 0 ≤ p ≤ 1.</param>
         /// <param name="n">The number of trials (n). Range: n ≥ 0.</param>
         /// <returns>The number of successes in <paramref name="n"/> trials.</returns>
@@ -384,7 +399,6 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Samples a sequence of binomially distributed random variable.
         /// </summary>
-        /// <param name="rnd">The random number generator to use.</param>
         /// <param name="p">The success probability (p) in each trial. Range: 0 ≤ p ≤ 1.</param>
         /// <param name="n">The number of trials (n). Range: n ≥ 0.</param>
         /// <returns>a sequence of successes in <paramref name="n"/> trials.</returns>

src/Numerics/Distributions/Categorical.cs

@@ -277,9 +277,9 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Gets the median of the distribution.
         /// </summary>
-        public int Median
+        public double Median
         {
-            get { return (int) _pmfNormalized.Median(); }
+            get { return _pmfNormalized.Median(); }
         }
 
         /// <summary>

src/Numerics/Distributions/Cauchy.cs

@@ -386,6 +386,7 @@ namespace MathNet.Numerics.Distributions
         /// Fills an array with samples generated from the distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
+        /// <param name="values">The array to fill with the samples.</param>
         /// <param name="location">The location (x0) of the distribution.</param>
         /// <param name="scale">The scale (γ) of the distribution. Range: γ > 0.</param>
         /// <returns>a sequence of samples from the distribution.</returns>
@@ -425,7 +426,7 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Fills an array with samples generated from the distribution.
         /// </summary>
-        /// <param name="rnd">The random number generator to use.</param>
+        /// <param name="values">The array to fill with the samples.</param>
         /// <param name="location">The location (x0) of the distribution.</param>
         /// <param name="scale">The scale (γ) of the distribution. Range: γ > 0.</param>
         /// <returns>a sequence of samples from the distribution.</returns>

src/Numerics/Distributions/ConwayMaxwellPoisson.cs

@@ -309,7 +309,7 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Gets the median of the distribution.
         /// </summary>
-        public int Median
+        public double Median
         {
             get { throw new NotSupportedException(); }
         }

src/Numerics/Distributions/DiscreteUniform.cs

@@ -193,9 +193,9 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Gets the median of the distribution.
         /// </summary>
-        public int Median
+        public double Median
         {
-            get { return (int)Math.Floor((_lower + _upper)/2.0); }
+            get { return (_lower + _upper)/2.0; }
         }
 
         /// <summary>

src/Numerics/Distributions/Geometric.cs

@@ -162,9 +162,9 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Gets the median of the distribution.
         /// </summary>
-        public int Median
+        public double Median
         {
-            get { return (int)Math.Ceiling(-Constants.Ln2/Math.Log(1 - _p)); }
+            get { return _p == 0.0 ? double.PositiveInfinity : _p == 1.0 ? 1.0 : Math.Ceiling(-Constants.Ln2/Math.Log(1 - _p)); }
         }
 
         /// <summary>

src/Numerics/Distributions/Hypergeometric.cs

@@ -222,7 +222,7 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Gets the median of the distribution.
         /// </summary>
-        public int Median
+        public double Median
         {
             get { throw new NotSupportedException(); }
         }

src/Numerics/Distributions/IContinuousDistribution.cs

@@ -43,11 +43,6 @@ namespace MathNet.Numerics.Distributions
         /// </summary>
         double Mode { get; }
 
-        /// <summary>
-        /// Gets the median of the distribution.
-        /// </summary>
-        double Median { get; }
-
         /// <summary>
         /// Gets the smallest element in the domain of the distribution which can be represented by a double.
         /// </summary>

src/Numerics/Distributions/IDiscreteDistribution.cs

@@ -43,11 +43,6 @@ namespace MathNet.Numerics.Distributions
         /// </summary>
         int Mode { get; }
 
-        /// <summary>
-        /// Gets the median of the distribution.
-        /// </summary>
-        int Median { get; }
-
         /// <summary>
         /// Gets the smallest element in the domain of the distribution which can be represented by an integer.
         /// </summary>

src/Numerics/Distributions/IUnivariateDistribution.cs

@@ -62,6 +62,11 @@ namespace MathNet.Numerics.Distributions
         /// </summary>
         double Skewness { get; }
 
+        /// <summary>
+        /// Gets the median of the distribution.
+        /// </summary>
+        double Median { get; }
+
         /// <summary>
         /// Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
         /// </summary>

src/Numerics/Distributions/Laplace.cs

@@ -407,7 +407,6 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Fills an array with samples generated from the distribution.
         /// </summary>
-        /// <param name="rnd">The random number generator to use.</param>
         /// <param name="values">The array to fill with the samples.</param>
         /// <param name="location">The location (μ) of the distribution.</param>
         /// <param name="scale">The scale (b) of the distribution. Range: b > 0.</param>

src/Numerics/Distributions/NegativeBinomial.cs

@@ -178,7 +178,7 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Gets the median of the distribution.
         /// </summary>
-        public int Median
+        public double Median
         {
             get { throw new NotSupportedException(); }
         }

src/Numerics/Distributions/Poisson.cs

@@ -185,9 +185,9 @@ namespace MathNet.Numerics.Distributions
         /// Gets the median of the distribution.
         /// </summary>
         /// <remarks>Approximation, see Wikipedia <a href="http://en.wikipedia.org/wiki/Poisson_distribution">Poisson distribution</a></remarks>
-        public int Median
+        public double Median
         {
-            get { return (int)Math.Floor(_lambda + (1.0/3.0) - (0.02/_lambda)); }
+            get { return Math.Floor(_lambda + (1.0/3.0) - (0.02/_lambda)); }
         }
 
         /// <summary>

src/Numerics/Distributions/Rayleigh.cs

@@ -397,7 +397,6 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Fills an array with samples generated from the distribution.
         /// </summary>
-        /// <param name="rnd">The random number generator to use.</param>
         /// <param name="values">The array to fill with the samples.</param>
         /// <param name="scale">The scale (σ) of the distribution. Range: σ > 0.</param>
         /// <returns>a sequence of samples from the distribution.</returns>

src/Numerics/Distributions/Triangular.cs

@@ -448,6 +448,7 @@ namespace MathNet.Numerics.Distributions
         /// Fills an array with samples generated from the distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
+        /// <param name="values">The array to fill with the samples.</param>
         /// <param name="lower">Lower bound. Range: lower ≤ mode ≤ upper</param>
         /// <param name="upper">Upper bound. Range: lower ≤ mode ≤ upper</param>
         /// <param name="mode">Mode (most frequent value).  Range: lower ≤ mode ≤ upper</param>
@@ -490,7 +491,7 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Fills an array with samples generated from the distribution.
         /// </summary>
-        /// <param name="rnd">The random number generator to use.</param>
+        /// <param name="values">The array to fill with the samples.</param>
         /// <param name="lower">Lower bound. Range: lower ≤ mode ≤ upper</param>
         /// <param name="upper">Upper bound. Range: lower ≤ mode ≤ upper</param>
         /// <param name="mode">Mode (most frequent value).  Range: lower ≤ mode ≤ upper</param>

src/Numerics/Distributions/Weibull.cs

@@ -425,6 +425,7 @@ namespace MathNet.Numerics.Distributions
         /// Fills an array with samples generated from the distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
+        /// <param name="values">The array to fill with the samples.</param>
         /// <param name="shape">The shape (k) of the Weibull distribution. Range: k > 0.</param>
         /// <param name="scale">The scale (λ) of the Weibull distribution. Range: λ > 0.</param>
         /// <returns>a sequence of samples from the distribution.</returns>
@@ -464,6 +465,7 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Fills an array with samples generated from the distribution.
         /// </summary>
+        /// <param name="values">The array to fill with the samples.</param>
         /// <param name="shape">The shape (k) of the Weibull distribution. Range: k > 0.</param>
         /// <param name="scale">The scale (λ) of the Weibull distribution. Range: λ > 0.</param>
         /// <returns>a sequence of samples from the distribution.</returns>

src/Numerics/Distributions/Zipf.cs

@@ -211,7 +211,7 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Gets the median of the distribution.
         /// </summary>
-        public int Median
+        public double Median
         {
             get { throw new NotSupportedException(); }
         }

src/UnitTests/DistributionTests/Discrete/BernoulliTests.cs

@@ -144,14 +144,14 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Discrete
             Assert.AreEqual(m, b.Mode);
         }
 
-        /// <summary>
+        [TestCase(0.0, 0.0)]
-        /// Validate median throws <c>NotSupportedException</c>.
+        [TestCase(0.4, 0.0)]
-        /// </summary>
+        [TestCase(0.5, 0.5)]
-        [Test]
+        [TestCase(0.6, 1.0)]
-        public void ValidateMedianThrowsNotSupportedException()
+        [TestCase(1.0, 1.0)]
+        public void ValidateMedian(double p, double expected)
         {
-            var b = new Bernoulli(0.3);
+            Assert.That(new Bernoulli(p).Median, Is.EqualTo(expected));
-            Assert.Throws<NotSupportedException>(() => { double m = b.Median; });
         }
 
         /// <summary>

src/UnitTests/DistributionTests/Discrete/GeometricTests.cs

@@ -143,17 +143,15 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Discrete
             Assert.AreEqual(1, d.Mode);
         }
 
-        /// <summary>
+        [TestCase(0.0, double.PositiveInfinity)]
-        /// Validate median.
+        [TestCase(0.0001, 6932.0)]
-        /// </summary>
+        [TestCase(0.1, 7.0)]
-        /// <param name="p">Probability of generating a one.</param>
+        [TestCase(0.3, 2.0)]
-        [TestCase(0.0)]
+        [TestCase(0.9, 1.0)]
-        [TestCase(0.3)]
+        [TestCase(1.0, 1.0)]
-        [TestCase(1.0)]
+        public void ValidateMedian(double p, double expected)
-        public void ValidateMedian(double p)
         {
-            var d = new Geometric(p);
+            Assert.That(new Geometric(p).Median, Is.EqualTo(expected));
-            Assert.AreEqual((int)Math.Ceiling(-Math.Log(2.0) / Math.Log(1 - p)), d.Median);
         }
 
         /// <summary>