public static int GeneratedWeighted_RND(List <double> Items)
{
// set up a discrete uniform distrubution
double max = Items.Max();
for (int i = 0; i < Items.Count; i++)
{
//Normal Distrubution = new Normal();
Poisson Distrubution = new Poisson(1);
//DiscreteUniform Distrubution = new DiscreteUniform(0,1);
Items[i] = Distrubution.CumulativeDistribution(Items[i]);
}
double cumulatedProbability = random.NextDouble() * Items.Sum();
for (int i = 0; i < Items.Count; i++)
{
if ((cumulatedProbability -= Items[i]) <= 0)
{
return(i);
}
}
throw new InvalidOperationException();
}
public void ValidateCumulativeDistribution(
[Values(1.5, 1.5, 1.5, 5.4, 5.4, 5.4, 10.8, 10.8, 10.8)] double lambda,
[Values(1, 10, 20, 1, 10, 20, 1, 10, 20)] int x,
[Values(0.5578254003710750000000, 0.9999994482467640000000, 1.0000000000000000000000, 0.0289061180327211000000, 0.9774863006897650000000, 0.9999997199928290000000, 0.0002407141402518290000, 0.4839692359955690000000, 0.9961800769608090000000)] double result)
{
var d = new Poisson(lambda);
Assert.AreEqual(d.CumulativeDistribution(x), result, 1e-12);
}
public int NumberOfArrival()
{
double randomNumber = rand.NextDouble();
int k = 0;
while (poisson.CumulativeDistribution(k) <= randomNumber)
{
k++;
}
return(k);
}
public override void ExecuteExample()
{
// <a href="http://en.wikipedia.org/wiki/Binomial_distribution">Binomial distribution</a>
MathDisplay.WriteLine("<b>Binomial distribution</b>");
// 1. Initialize the new instance of the Binomial distribution class with parameters P = 0.2, N = 20
var binomial = new Binomial(0.2, 20);
MathDisplay.WriteLine(@"1. Initialize the new instance of the Binomial distribution class with parameters P = {0}, N = {1}", binomial.P, binomial.N);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", binomial);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", binomial.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", binomial.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", binomial.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
MathDisplay.WriteLine(@"{0} - Entropy", binomial.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", binomial.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", binomial.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", binomial.Mean.ToString(" #0.00000;-#0.00000"));
// Median
MathDisplay.WriteLine(@"{0} - Median", binomial.Median.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", binomial.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", binomial.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", binomial.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", binomial.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the Binomial distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the Binomial distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(binomial.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Bernoulli_distribution">Bernoulli distribution</a>
MathDisplay.WriteLine("<b>Bernoulli distribution</b>");
// 1. Initialize the new instance of the Bernoulli distribution class with parameter P = 0.2
var bernoulli = new Bernoulli(0.2);
MathDisplay.WriteLine(@"1. Initialize the new instance of the Bernoulli distribution class with parameter P = {0}", bernoulli.P);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", bernoulli);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", bernoulli.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", bernoulli.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", bernoulli.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
MathDisplay.WriteLine(@"{0} - Entropy", bernoulli.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", bernoulli.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", bernoulli.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", bernoulli.Mean.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", bernoulli.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", bernoulli.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", bernoulli.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", bernoulli.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the Bernoulli distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the Bernoulli distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(bernoulli.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Categorical_distribution">Categorical distribution</a>
MathDisplay.WriteLine("<b>Categorical distribution</b>");
// 1. Initialize the new instance of the Categorical distribution class with parameters P = (0.1, 0.2, 0.25, 0.45)
var binomialC = new Categorical(new[] { 0.1, 0.2, 0.25, 0.45 });
MathDisplay.WriteLine(@"1. Initialize the new instance of the Categorical distribution class with parameters P = (0.1, 0.2, 0.25, 0.45)");
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", binomialC);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", binomialC.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", binomialC.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", binomialC.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
MathDisplay.WriteLine(@"{0} - Entropy", binomialC.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", binomialC.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", binomialC.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", binomialC.Mean.ToString(" #0.00000;-#0.00000"));
// Median
MathDisplay.WriteLine(@"{0} - Median", binomialC.Median.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", binomialC.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", binomialC.StdDev.ToString(" #0.00000;-#0.00000"));
// 3. Generate 10 samples of the Categorical distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the Categorical distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(binomialC.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Conway%E2%80%93Maxwell%E2%80%93Poisson_distribution">ConwayMaxwellPoisson distribution</a>
MathDisplay.WriteLine("<b>Conway Maxwell Poisson distribution</b>");
// 1. Initialize the new instance of the ConwayMaxwellPoisson distribution class with parameters Lambda = 2, Nu = 1
var conwayMaxwellPoisson = new ConwayMaxwellPoisson(2, 1);
MathDisplay.WriteLine(@"1. Initialize the new instance of the ConwayMaxwellPoisson distribution class with parameters Lambda = {0}, Nu = {1}", conwayMaxwellPoisson.Lambda, conwayMaxwellPoisson.Nu);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", conwayMaxwellPoisson);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", conwayMaxwellPoisson.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", conwayMaxwellPoisson.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", conwayMaxwellPoisson.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", conwayMaxwellPoisson.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", conwayMaxwellPoisson.Mean.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", conwayMaxwellPoisson.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", conwayMaxwellPoisson.StdDev.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the ConwayMaxwellPoisson distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the ConwayMaxwellPoisson distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(conwayMaxwellPoisson.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Discrete_uniform">DiscreteUniform distribution</a>
MathDisplay.WriteLine("<b>Discrete Uniform distribution</b>");
// 1. Initialize the new instance of the DiscreteUniform distribution class with parameters LowerBound = 2, UpperBound = 10
var discreteUniform = new DiscreteUniform(2, 10);
MathDisplay.WriteLine(@"1. Initialize the new instance of the DiscreteUniform distribution class with parameters LowerBound = {0}, UpperBound = {1}", discreteUniform.LowerBound, discreteUniform.UpperBound);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", discreteUniform);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", discreteUniform.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", discreteUniform.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", discreteUniform.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
MathDisplay.WriteLine(@"{0} - Entropy", discreteUniform.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", discreteUniform.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", discreteUniform.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", discreteUniform.Mean.ToString(" #0.00000;-#0.00000"));
// Median
MathDisplay.WriteLine(@"{0} - Median", discreteUniform.Median.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", discreteUniform.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", discreteUniform.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", discreteUniform.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", discreteUniform.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the DiscreteUniform distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the DiscreteUniform distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(discreteUniform.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Geometric_distribution">Geometric distribution</a>
MathDisplay.WriteLine("<b>Geometric distribution</b>");
// 1. Initialize the new instance of the Geometric distribution class with parameter P = 0.2
var geometric = new Geometric(0.2);
MathDisplay.WriteLine(@"1. Initialize the new instance of the Geometric distribution class with parameter P = {0}", geometric.P);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", geometric);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", geometric.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", geometric.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", geometric.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
MathDisplay.WriteLine(@"{0} - Entropy", geometric.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", geometric.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", geometric.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", geometric.Mean.ToString(" #0.00000;-#0.00000"));
// Median
MathDisplay.WriteLine(@"{0} - Median", geometric.Median.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", geometric.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", geometric.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", geometric.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", geometric.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the Geometric distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the Geometric distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(geometric.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Hypergeometric_distribution">Hypergeometric distribution</a>
MathDisplay.WriteLine("<b>Hypergeometric distribution</b>");
// 1. Initialize the new instance of the Hypergeometric distribution class with parameters PopulationSize = 10, M = 2, N = 8
var hypergeometric = new Hypergeometric(30, 15, 10);
MathDisplay.WriteLine(@"1. Initialize the new instance of the Hypergeometric distribution class with parameters Population = {0}, Success = {1}, Draws = {2}", hypergeometric.Population, hypergeometric.Success, hypergeometric.Draws);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", hypergeometric);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", hypergeometric.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", hypergeometric.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", hypergeometric.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", hypergeometric.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", hypergeometric.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", hypergeometric.Mean.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", hypergeometric.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", hypergeometric.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", hypergeometric.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", hypergeometric.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the Hypergeometric distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the Hypergeometric distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(hypergeometric.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Negative_binomial">NegativeBinomial distribution</a>
MathDisplay.WriteLine("<b>Negative Binomial distribution</b>");
// 1. Initialize the new instance of the NegativeBinomial distribution class with parameters P = 0.2, R = 20
var negativeBinomial = new NegativeBinomial(20, 0.2);
MathDisplay.WriteLine(@"1. Initialize the new instance of the NegativeBinomial distribution class with parameters P = {0}, N = {1}", negativeBinomial.P, negativeBinomial.R);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", negativeBinomial);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", negativeBinomial.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", negativeBinomial.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", negativeBinomial.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", negativeBinomial.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", negativeBinomial.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", negativeBinomial.Mean.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", negativeBinomial.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", negativeBinomial.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", negativeBinomial.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", negativeBinomial.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the NegativeBinomial distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the NegativeBinomial distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(negativeBinomial.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Poisson_distribution">Poisson distribution</a>
MathDisplay.WriteLine("<b>Poisson distribution</b>");
// 1. Initialize the new instance of the Poisson distribution class with parameter Lambda = 1
var poisson = new Poisson(1);
MathDisplay.WriteLine(@"1. Initialize the new instance of the Poisson distribution class with parameter Lambda = {0}", poisson.Lambda);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", poisson);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", poisson.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", poisson.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", poisson.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
MathDisplay.WriteLine(@"{0} - Entropy", poisson.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", poisson.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", poisson.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", poisson.Mean.ToString(" #0.00000;-#0.00000"));
// Median
MathDisplay.WriteLine(@"{0} - Median", poisson.Median.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", poisson.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", poisson.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", poisson.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", poisson.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the Poisson distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the Poisson distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(poisson.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Zipf_distribution">Zipf distribution</a>
MathDisplay.WriteLine("<b>Zipf distribution</b>");
// 1. Initialize the new instance of the Zipf distribution class with parameters S = 5, N = 10
var zipf = new Zipf(5, 10);
MathDisplay.WriteLine(@"1. Initialize the new instance of the Zipf distribution class with parameters S = {0}, N = {1}", zipf.S, zipf.N);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", zipf);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", zipf.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", zipf.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", zipf.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
MathDisplay.WriteLine(@"{0} - Entropy", zipf.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", zipf.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", zipf.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", zipf.Mean.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", zipf.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", zipf.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", zipf.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", zipf.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the Zipf distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the Zipf distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(zipf.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
}
/// <summary>
/// Run example
/// </summary>
/// <a href="http://en.wikipedia.org/wiki/Poisson_distribution">Poisson distribution</a>
public void Run()
{
// 1. Initialize the new instance of the Poisson distribution class with parameter Lambda = 1
var poisson = new Poisson(1);
Console.WriteLine(@"1. Initialize the new instance of the Poisson distribution class with parameter Lambda = {0}", poisson.Lambda);
Console.WriteLine();
// 2. Distributuion properties:
Console.WriteLine(@"2. {0} distributuion properties:", poisson);
// Cumulative distribution function
Console.WriteLine(@"{0} - Сumulative distribution at location '3'", poisson.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
Console.WriteLine(@"{0} - Probability mass at location '3'", poisson.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
Console.WriteLine(@"{0} - Log probability mass at location '3'", poisson.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
Console.WriteLine(@"{0} - Entropy", poisson.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
Console.WriteLine(@"{0} - Largest element in the domain", poisson.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
Console.WriteLine(@"{0} - Smallest element in the domain", poisson.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
Console.WriteLine(@"{0} - Mean", poisson.Mean.ToString(" #0.00000;-#0.00000"));
// Median
Console.WriteLine(@"{0} - Median", poisson.Median.ToString(" #0.00000;-#0.00000"));
// Mode
Console.WriteLine(@"{0} - Mode", poisson.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
Console.WriteLine(@"{0} - Variance", poisson.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
Console.WriteLine(@"{0} - Standard deviation", poisson.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
Console.WriteLine(@"{0} - Skewness", poisson.Skewness.ToString(" #0.00000;-#0.00000"));
Console.WriteLine();
// 3. Generate 10 samples of the Poisson distribution
Console.WriteLine(@"3. Generate 10 samples of the Poisson distribution");
for (var i = 0; i < 10; i++)
{
Console.Write(poisson.Sample().ToString("N05") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 4. Generate 100000 samples of the Poisson(1) distribution and display histogram
Console.WriteLine(@"4. Generate 100000 samples of the Poisson(1) distribution and display histogram");
var data = new double[100000];
for (var i = 0; i < data.Length; i++)
{
data[i] = poisson.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 5. Generate 100000 samples of the Poisson(4) distribution and display histogram
Console.WriteLine(@"5. Generate 100000 samples of the Poisson(4) distribution and display histogram");
poisson.Lambda = 4;
for (var i = 0; i < data.Length; i++)
{
data[i] = poisson.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 6. Generate 100000 samples of the Poisson(10) distribution and display histogram
Console.WriteLine(@"6. Generate 100000 samples of the Poisson(10) distribution and display histogram");
poisson.Lambda = 10;
for (var i = 0; i < data.Length; i++)
{
data[i] = poisson.Sample();
}
ConsoleHelper.DisplayHistogram(data);
}
public void ValidateCumulativeDistribution(double lambda, int x, double result)
{
var d = new Poisson(lambda);
Assert.AreEqual(d.CumulativeDistribution(x), result, 1e-12);
}
public void ValidateCumulativeDistribution(double lambda, int x, double result)
{
var d = new Poisson(lambda);
Assert.AreApproximatelyEqual(d.CumulativeDistribution(x), result, 1e-12);
}
public void ValidateCumulativeDistribution(
[Values(1.5, 1.5, 1.5, 5.4, 5.4, 5.4, 10.8, 10.8, 10.8)] double lambda,
[Values(1, 10, 20, 1, 10, 20, 1, 10, 20)] int x,
[Values(0.5578254003710750000000, 0.9999994482467640000000, 1.0000000000000000000000, 0.0289061180327211000000, 0.9774863006897650000000, 0.9999997199928290000000, 0.0002407141402518290000, 0.4839692359955690000000, 0.9961800769608090000000)] double result)
{
var d = new Poisson(lambda);
Assert.AreEqual(d.CumulativeDistribution(x), result, 1e-12);
}
private void obtenerFrecuenciasEsperadas()
{
double media = MathNet.Numerics.Statistics.ArrayStatistics.Mean(datos.ToArray());
switch (distribucionElegida)
{
case TipoDistribucion.continuaExponencial:
/*
* En el caso de haber elegido la distribucion exponencial, tenemos que:
*
* lambda(media) = 1 / (media muestral);
*
*/
//obtenemos el lambda para esta distribucion
double lambda = 1 / media;
//generamos la distribucion para el lambda dado:
Exponential exponencial = new Exponential(lambda);
//recorremos los intervalos para obtener los valores minimos y maximos, y asi calcular la frecuencia esperada
foreach (Intervalo intervalo in intervalos)
{
intervalo.frecuenciaEsperada = (exponencial.CumulativeDistribution(intervalo.limiteSuperior) - exponencial.CumulativeDistribution(intervalo.limiteInferior)) * datos.Count();
intervalo.frecuenciaEsperada = Math.Round(intervalo.frecuenciaEsperada, CANTIDAD_DECIMALES);
}
break;
case TipoDistribucion.continuaUniforme:
/*
* En el caso de haber elegido uniforme, tenemos que:
*
* FE = cantidad de datos de la muestra / cantidad de intervalos;
*
*/
//Entonces obtenemos este dato y se lo asignamos a todos los intervalos.
double frecuenciaEsperada = (double)datos.Count() / (double)intervalos.Count();
foreach (Intervalo intervalo in intervalos)
{
intervalo.frecuenciaEsperada = frecuenciaEsperada;
intervalo.frecuenciaEsperada = Math.Round(intervalo.frecuenciaEsperada, CANTIDAD_DECIMALES);
}
break;
case TipoDistribucion.continuaNormal:
/*
* Para distribucion normal tenemos:
*
* desviacion estandar (sigma) = raiz cuadrada de la media;
*
*/
//obtenemos la varianza
double varianza = MathNet.Numerics.Statistics.ArrayStatistics.Variance(datos.ToArray());
//calculamos la deviacion estandar
double desviacionEstandar = Math.Sqrt(varianza);
//creo la distribucion normal
MathNet.Numerics.Distributions.Normal normal = new MathNet.Numerics.Distributions.Normal(media, desviacionEstandar);
foreach (Intervalo intervalo in intervalos)
{
intervalo.frecuenciaEsperada = (normal.CumulativeDistribution(intervalo.limiteSuperior) - normal.CumulativeDistribution(intervalo.limiteInferior)) * datos.Count();
intervalo.frecuenciaEsperada = Math.Round(intervalo.frecuenciaEsperada, CANTIDAD_DECIMALES);
}
break;
case TipoDistribucion.continuaPoisson:
double lambdaPoisson = 1 / media;
Poisson poisson = new Poisson(media);
//recorremos los intervalos para obtener los valores minimos y maximos, y asi calcular la frecuencia esperada
foreach (Intervalo intervalo in intervalos)
{
intervalo.frecuenciaEsperada = (poisson.CumulativeDistribution(intervalo.limiteInferior) - poisson.CumulativeDistribution(intervalo.limiteInferior - 1)) * datos.Count();
intervalo.frecuenciaEsperada = Math.Round(intervalo.frecuenciaEsperada, CANTIDAD_DECIMALES);
}
break;
}
}
