Fixed bugs after running the Sample unit tests.

Fixed some spelling mistakes.
Changed the Histogram implementation to make lowerbound exclusive and upper bound inclusive. [http://mathnetnumerics.codeplex.com/Thread/View.aspx?ThreadId=75115]
Changed the Histogram implementation so that returned buckets are copies (so that users can't start messing with upper and lower bounds).

Signed-off-by: jvangael <jurgen.vangael@gmail.com>

src/Numerics/Distributions/Discrete/Binomial.cs

@@ -255,8 +255,13 @@ namespace MathNet.Numerics.Distributions
                 return 1.0;
             }
 
-            int k = (int) Math.Floor(x);
-            return (_n - k) * Combinatorics.Combinations(_n,k) * SpecialFunctions.BetaRegularized(_n - k, 1 + k, 1-_p);
+            double cdf = 0.0;
+            for (int i = 0; i <= (int) Math.Floor(x); i++)
+            {
+                cdf += Combinatorics.Combinations(_n, i) * Math.Pow(_p, i) * Math.Pow(1.0 - _p, _n - i);
+            }
+
+            return cdf;
         }
 
         #endregion
@@ -366,7 +371,7 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Samples a Binomially distributed random variable.
         /// </summary>
-        /// <returns>The number of successful trials.</returns>
+        /// <returns>The number of successes in <paramref name="n"/> trials.</returns>
         public int Sample()
         {
             return DoSample(RandomSource, _p, _n);
@@ -375,7 +380,7 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Samples an array of Bernoulli distributed random variables.
         /// </summary>
-        /// <returns>a sequence of successful trial counts.</returns>
+        /// <returns>a sequence of successes in <paramref name="n"/> trials.</returns>
         public IEnumerable<int> Samples()
         {
             while (true)
@@ -392,7 +397,7 @@ namespace MathNet.Numerics.Distributions
         /// <param name="rnd">The random number generator to use.</param>
         /// <param name="p">The success probability of a trial; must be in the interval [0.0, 1.0].</param>
         /// <param name="n">The number of trials; must be positive.</param>
-        /// <returns>The number of successes in <see cref="N"/> trials.</returns>
+        /// <returns>The number of successes in <paramref name="n"/> trials.</returns>
         public static int Sample(System.Random rnd, double p, int n)
         {
             if (Control.CheckDistributionParameters && !IsValidParameterSet(p, n))
@@ -409,7 +414,7 @@ namespace MathNet.Numerics.Distributions
         /// <param name="rnd">The random number generator to use.</param>
         /// <param name="p">The success probability of a trial; must be in the interval [0.0, 1.0].</param>
         /// <param name="n">The number of trials; must be positive.</param>
-        /// <returns>a sequence of successful trial counts.</returns>
+        /// <returns>a sequence of successes in <paramref name="n"/> trials.</returns>
         public static IEnumerable<int> Samples(System.Random rnd, double p, int n)
         {
             if (Control.CheckDistributionParameters && !IsValidParameterSet(p, n))

src/Numerics/Distributions/Discrete/Categorical.cs

@@ -322,7 +322,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>The number of successful trials.</returns>
         public int Sample()
         {
-            return DoSample(RandomSource, _p);
+            return Sample(RandomSource, _p);
         }
 
         /// <summary>
@@ -331,10 +331,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a sequence of successful trial counts.</returns>
         public IEnumerable<int> Samples()
         {
-            while (true)
-            {
-                yield return DoSample(RandomSource, _p);
-            }
+            return Samples(RandomSource, _p);
         }
 
         #endregion

src/Numerics/Statistics/Histogram.cs

@@ -35,10 +35,10 @@ namespace MathNet.Numerics.Statistics
 
     /// <summary>
     /// A <see cref="Histogram"/> consists of a series of <see cref="Bucket"/>s, 
-    /// each representing a region limited by a lower bound (inclusive) and an upper bound (exclusive).
+    /// each representing a region limited by a lower bound (exclusive) and an upper bound (inclusive).
     /// </summary>
     [Serializable]
-    public class Bucket : IComparable<Bucket>
+    public class Bucket : IComparable<Bucket>, ICloneable
     {
         /// <summary>
         /// This <c>IComparer</c> performs comparisons between a point and a bucket.
@@ -55,11 +55,11 @@ namespace MathNet.Numerics.Statistics
             {
                 if (bkt2.Width == 0.0)
                 {
-                    return -bkt1.Contains(bkt2.LowerBound);
+                    return -bkt1.Contains(bkt2.UpperBound);
                 }
                 else
                 {
-                    return -bkt2.Contains(bkt1.LowerBound);
+                    return -bkt2.Contains(bkt1.UpperBound);
                 }
             }
         }
@@ -108,6 +108,15 @@ namespace MathNet.Numerics.Statistics
             Count = count;
         }
 
+        /// <summary>
+        /// Creates a copy of the Bucket with the lowerbound, upperbound and counts exactly equal.
+        /// </summary>
+        /// <returns>A cloned Bucket object.</returns>
+        public Object Clone()
+        {
+            return new Bucket(LowerBound, UpperBound, Count);
+        }
+
         /// <summary>
         /// Width of the Bucket.
         /// </summary>
@@ -132,9 +141,9 @@ namespace MathNet.Numerics.Statistics
         /// smaller than the bucket, +1 if the point is larger than the bucket.</returns>
         public int Contains(double x)
         {
-            if (LowerBound <= x)
+            if (LowerBound < x)
             {
-                if (UpperBound > x)
+                if (UpperBound >= x)
                 {
                     return 0;
                 }
@@ -146,7 +155,7 @@ namespace MathNet.Numerics.Statistics
         }
 
         /// <summary>
-        /// Comparison of two disjoint buckets.
+        /// Comparison of two disjoint buckets. The buckets cannot be overlapping.
         /// </summary>
         public int CompareTo(Bucket bucket)
         {
@@ -200,7 +209,7 @@ namespace MathNet.Numerics.Statistics
         /// <returns></returns>
         public override string ToString()
         {
-            return "[" + this.LowerBound + ";" + this.UpperBound + ")";
+            return "(" + this.LowerBound + ";" + this.UpperBound + "] = " + this.Count;
         }
     }
     
@@ -247,12 +256,13 @@ namespace MathNet.Numerics.Statistics
             double upper = data.Maximum();
             double width = (upper - lower) / nbuckets;
 
-            // Add buckets for each bin; the biggest bucket must be slightly larger then the maximal element.
-            for (int n = 0; n < nbuckets-1; n++)
+            // Add buckets for each bin; the smallest bucket's lowerbound must be slightly smaller
+            // than the minimal element.
+            AddBucket(new Bucket(lower.Decrement(), lower + width));
+            for (int n = 1; n < nbuckets; n++)
             {
                 AddBucket(new Bucket(lower + n * width, lower + (n + 1) * width));
             }
-            AddBucket(new Bucket(lower + (nbuckets - 1) * width, upper.Increment()));
 
             AddData(data);
         }
@@ -294,20 +304,23 @@ namespace MathNet.Numerics.Statistics
         /// <param name="d">The datapoint which we want to add.</param>
         public void AddData(double d)
         {
+            // Sort if needed.
+            LazySort();
+
             if (d < this.LowerBound)
             {
-                this[0].LowerBound = d;
-                this[0].Count++;
+                // Make the lower bound just slightly smaller than the datapoint so it is contained in this bucket.
+                buckets[0].LowerBound = d.Decrement();
+                buckets[0].Count++;
             }
             else if (d > this.UpperBound)
             {
-                // Make the upper bound just slightly larger then the datapoint so it is contained in this bucket.
-                this[BucketCount - 1].UpperBound = d.Increment();
-                this[BucketCount - 1].Count++;
+                buckets[BucketCount - 1].UpperBound = d;
+                buckets[BucketCount - 1].Count++;
             }
             else
             {
-                GetBucketOf(d).Count++;
+                buckets[GetBucketIndexOf(d)].Count++;
             }
         }
 
@@ -345,24 +358,14 @@ namespace MathNet.Numerics.Statistics
             }
         }
 
-        /// <summary>
-        /// Returns the <c>Bucket</c> with index <paramref name="i"/>.
-        /// </summary>
-        /// <param name="i">The index of the bucket to retrieve.</param>
-        /// <returns>A reference to the bucket at index <paramref name="i"/>.</returns>
-        public Bucket GetBucket(int i)
-        {
-            return buckets[i];
-        }
-
         /// <summary>
         /// Returns the <c>Bucket</c> that contains the value <c>v</c>. 
         /// </summary>
         /// <param name="v">The point to search the bucket for.</param>
-        /// <returns>The bucket containing the point.</returns>
+        /// <returns>A copy of the bucket containing point <paramref name="v"/>.</returns>
         public Bucket GetBucketOf(double v)
         {
-            return buckets[GetBucketIndexOf(v)];
+            return (Bucket) buckets[GetBucketIndexOf(v)].Clone();
         }
 
         /// <summary>
@@ -415,13 +418,13 @@ namespace MathNet.Numerics.Statistics
         /// Gets the <c>n</c>'th bucket.
         /// </summary>
         /// <param name="n">The index of the bucket to be returned.</param>
-        /// <returns>The <c>n</c>'th bucket.</returns>
+        /// <returns>A copy of the <c>n</c>'th bucket.</returns>
         public Bucket this[int n]
         {
             get
             {
                 LazySort();
-                return buckets[n];
+                return (Bucket) buckets[n].Clone();
             }
         }
         

src/UnitTests/DistributionTests/CommonDistributionTests.cs

@@ -32,8 +32,9 @@ namespace MathNet.Numerics.UnitTests.DistributionTests
     using System.Linq;
     using System.Collections.Generic;
     using MbUnit.Framework;
-    using MathNet.Numerics.Distributions;
+    using MathNet.Numerics.Random;
     using MathNet.Numerics.Statistics;
+    using MathNet.Numerics.Distributions;
 
     [TestFixture]
     public class CommonDistributionTests
@@ -116,29 +117,34 @@ namespace MathNet.Numerics.UnitTests.DistributionTests
         [MultipleAsserts]
         public void SampleFollowsCorrectDistribution()
         {
+            Random rnd = new MersenneTwister();
+
             // The test samples from the distributions, builds a histogram and checks
             // whether the histogram follows the CDF.
             foreach (var dd in discreteDistributions)
             {
-                int[] samples = new int[numberOfTestSamples];
+                dd.RandomSource = rnd;
+
+                double[] samples = new double[numberOfTestSamples];
                 for (int i = 0; i < numberOfTestSamples; i++)
                 {
-                    samples[i] = dd.Sample();
+                    samples[i] = (double) dd.Sample();
                 }
 
-                var histogram = new Histogram(samples.Select(x => (double)x), numberOfBuckets);
+                var histogram = new Histogram(samples, numberOfBuckets);
                 for (int i = 0; i < numberOfBuckets; i++)
                 {
-                    var bucket = histogram.GetBucket(i);
+                    var bucket = histogram[i];
                     double empiricalProbability = bucket.Count / (double)numberOfTestSamples;
                     double realProbability = dd.CumulativeDistribution(bucket.UpperBound)
                         - dd.CumulativeDistribution(bucket.LowerBound);
-                    Assert.LessThan(Math.Abs(empiricalProbability - realProbability), sampleAccuracy);
+                    Assert.LessThan(Math.Abs(empiricalProbability - realProbability), sampleAccuracy, dd.ToString());
                 }
             }
 
             foreach (var cd in continuousDistributions)
             {
+                cd.RandomSource = rnd;
                 double[] samples = new double[numberOfTestSamples];
                 for (int i = 0; i < numberOfTestSamples; i++)
                 {
@@ -148,11 +154,11 @@ namespace MathNet.Numerics.UnitTests.DistributionTests
                 var histogram = new Histogram(samples, numberOfBuckets);
                 for (int i = 0; i < numberOfBuckets; i++)
                 {
-                    var bucket = histogram.GetBucket(i);
+                    var bucket = histogram[i];
                     double empiricalProbability = bucket.Count / (double)numberOfTestSamples;
                     double realProbability = cd.CumulativeDistribution(bucket.UpperBound)
                         - cd.CumulativeDistribution(bucket.LowerBound);
-                    Assert.LessThan(Math.Abs(empiricalProbability - realProbability), sampleAccuracy);
+                    Assert.LessThan(Math.Abs(empiricalProbability - realProbability), sampleAccuracy, cd.ToString());
                 }
             }
         }
@@ -161,35 +167,39 @@ namespace MathNet.Numerics.UnitTests.DistributionTests
         [MultipleAsserts]
         public void SamplesFollowsCorrectDistribution()
         {
+            Random rnd = new MersenneTwister();
+
             // The test samples from the distributions, builds a histogram and checks
             // whether the histogram follows the CDF.
             foreach (var dd in discreteDistributions)
             {
+                dd.RandomSource = rnd;
                 var samples = dd.Samples().Take(numberOfTestSamples).Select(x => (double)x);
 
                 var histogram = new Histogram(samples, numberOfBuckets);
                 for (int i = 0; i < numberOfBuckets; i++)
                 {
-                    var bucket = histogram.GetBucket(i);
+                    var bucket = histogram[i];
                     double empiricalProbability = bucket.Count / (double)numberOfTestSamples;
                     double realProbability = dd.CumulativeDistribution(bucket.UpperBound)
                         - dd.CumulativeDistribution(bucket.LowerBound);
-                    Assert.LessThan(Math.Abs(empiricalProbability - realProbability), sampleAccuracy);
+                    Assert.LessThan(Math.Abs(empiricalProbability - realProbability), sampleAccuracy, dd.ToString());
                 }
             }
 
             foreach (var cd in continuousDistributions)
             {
+                cd.RandomSource = rnd;
                 var samples = cd.Samples().Take(numberOfTestSamples);
 
                 var histogram = new Histogram(samples, numberOfBuckets);
                 for (int i = 0; i < numberOfBuckets; i++)
                 {
-                    var bucket = histogram.GetBucket(i);
+                    var bucket = histogram[i];
                     double empiricalProbability = bucket.Count / (double)numberOfTestSamples;
                     double realProbability = cd.CumulativeDistribution(bucket.UpperBound)
                         - cd.CumulativeDistribution(bucket.LowerBound);
-                    Assert.LessThan(Math.Abs(empiricalProbability - realProbability), sampleAccuracy);
+                    Assert.LessThan(Math.Abs(empiricalProbability - realProbability), sampleAccuracy, cd.ToString());
                 }
             }
         }

src/UnitTests/StatisticsTests/HistogramTests.cs

@@ -95,7 +95,9 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
         }
 
         [Test]
+        [Row(0.0, -1)]
         [Row(1.0, 0)]
+        [Row(1.5, 0)]
         [Row(2.0, 1)]
         [Row(-1.0, -1)]
         public void ValidateContains(double x, int r)
@@ -106,9 +108,8 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
 
         #endregion
 
+        #region Histogram Tests
 
-
-        #region
         [Test]
         public void CanCreateEmptyHistogram()
         {
@@ -123,9 +124,8 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
         }
 
         [Test]
-        [Row(0.0, 0)]
         [Row(0.5, 0)]
-        [Row(1.0, 1)]
+        [Row(1.0, 0)]
         [Row(10.0, 3)]
         [Row(10000.0, 4)]
         public void CanGetBucketIndexOf(double x, double i)
@@ -139,6 +139,21 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
             Assert.AreEqual(i, h.GetBucketIndexOf(x));
         }
 
+        [Test]
+        [Row(0.0)]
+        [Row(-1.0)]
+        [ExpectedArgumentException]
+        public void CanGetBucketIndexOfFailsWhenBucketDoesntExist(double x)
+        {
+            var h = new Histogram();
+            h.AddBucket(new Bucket(0.0, 1.0));
+            h.AddBucket(new Bucket(1.0, 2.0));
+            h.AddBucket(new Bucket(2.0, 3.0));
+            h.AddBucket(new Bucket(3.0, 20.0));
+            h.AddBucket(new Bucket(20.0, Double.PositiveInfinity));
+            int i = h.GetBucketIndexOf(x);
+        }
+
         [Test]
         public void CanGetBucketOf()
         {
@@ -256,18 +271,19 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
 
             Console.WriteLine("{0}", hist);
 
-            for (int i = 0; i < 8; i++)
+            for (int i = 1; i < 9; i++)
             {
                 Console.WriteLine("{0} : {1}", i, hist[i].Count);
                 Assert.AreEqual(1.0, hist[i].Count);
             }
-            Assert.AreEqual(2.0, hist[8].Count);
+            Assert.AreEqual(2.0, hist[0].Count);
 
-            Assert.AreEqual(0.5, hist.LowerBound);
-            Assert.AreEqual(9.5.Increment(), hist.UpperBound);
+            Assert.AreEqual(0.5.Decrement(), hist.LowerBound);
+            Assert.AreEqual(9.5, hist.UpperBound);
         }
 
         [Test]
+        [MultipleAsserts]
         public void SmallDatasetHistogramWithBounds()
         {
             Histogram hist = new Histogram(smallDataset, 10, 0.0, 10.0);