/// <summary>
/// This will show the poisson distribution
/// Question 3
/// Libraries and tool i used: MathNet
/// install using nugpack from visual studio
/// I have used code that was provided from
/// https://rosettacode.org/wiki/Statistics/Normal_distribution#C
/// I have modified the code to give me a poisson distribution
/// also comes with a histogram.
/// I have used the code given in this site for the solution of question 4
/// </summary>
/// <param name="numTrials">The number of number to generate</param>
/// <param name="lambda">The expected value</param>
static void Question4(int numTrials, int lambda)
{
int[] X = new int[numTrials]; //just an array to store the generated number
var poisson = new Poisson(5); //Create a new poisson object provided from the library
poisson.Samples(X); //Create the sample
double[] Y = new double[numTrials]; //For this part of the code because the histogram doesn't accept integer array i have to convert them into double
for (int i = 0; i < numTrials; i++) //By using this for loop and transfering the numbers into a double
{
Y[i] = X[i];
}
const int numBuckets = 10; //number of buckets
var histogram = new Histogram(Y, numBuckets); //The histogram will create a histogram based on the number of buckets and the sample array
Console.WriteLine("Sample size: {0:N0}", numTrials);
Console.WriteLine("The lambda value: {0}\n", lambda);
for (int i = 0; i < numBuckets; i++)
{
string bar = new String('#', (int)(histogram[i].Count * MAX_STAR / numTrials));
Console.WriteLine("bin" + i + " {0:0.00} \t: {1} {2: 0.00}%", histogram[i].LowerBound, bar, histogram[i].Count / numTrials);
}
Console.WriteLine();
}
public void CanSampleSequence()
{
var d = new Poisson(0.3);
var ied = d.Samples();
GC.KeepAlive(ied.Take(5).ToArray());
}
public int[] RandomSample(int sample_size)
{
int [] sample = new int [sample_size];
Random random = new Random();
Poisson.Samples(random, sample, d_lambda);
return(sample);
}
private static void GenerateJD_PriceMatrixValues(double volatility, double riskFreeOptionPrice, MersenneTwister random, double dT,
List <Tuple <double, double[]> > jdPriceMatrix, double jumpDrift, int simulations)
{
for (var i = 1; i < EnvironmentSettings.Instance.TimeIntervals + 1; i++)
{
var gaussPrice = Normal.WithMeanStdDev(0.0, 1.0, random).Samples().Take(simulations).ToArray();
var gaussJump = Normal.WithMeanStdDev(0.0, 1.0, random).Samples().Take(simulations).ToArray();
var poissonJump = Poisson.Samples(EnvironmentSettings.Instance.JumpLambda * dT).Take(simulations).ToArray();
var S = Simulation_JD(riskFreeOptionPrice, dT, volatility, gaussPrice, gaussJump,
poissonJump, jdPriceMatrix[i - 1], jumpDrift, simulations);
jdPriceMatrix.Add(new Tuple <double, double[]>(i * dT, S));
}
}
public void CanSampleSequence()
{
var d = new Poisson(0.3);
var ied = d.Samples();
ied.Take(5).ToArray();
}
public void CanSampleSequence()
{
var d = new Poisson(0.3);
var ied = d.Samples();
var e = ied.Take(5).ToArray();
}
public double[] GetSampleData(string distType, double mostLikelyEstimate,
double lowEstimate, double highEstimate)
{
if (Iterations > 10000)
{
Iterations = 10000;
}
if (Iterations <= 2)
{
Iterations = 1000;
}
if (this.CILevel < 10)
{
this.CILevel = 90;
}
if (this.CILevel > 99)
{
this.CILevel = 99;
}
Random rnd = new Random(Random);
mostLikelyEstimate = Math.Round(mostLikelyEstimate, 4);
lowEstimate = Math.Round(lowEstimate, 4);
highEstimate = Math.Round(highEstimate, 4);
var sampledata = new double[Iterations];
if (distType == Calculator1.RUC_TYPES.triangle.ToString())
{
if (lowEstimate >= mostLikelyEstimate || lowEstimate == 0)
{
//arbitrary rules (25%)
lowEstimate = mostLikelyEstimate * .75;
//no errors: lowEstimate = 0 is often the case
//sb.AppendLine(Errors.GetMessage("DATA_BADDISTRIBUTION"));
}
if (highEstimate <= mostLikelyEstimate || highEstimate == 0)
{
//arbitrary rules (25%)
highEstimate = mostLikelyEstimate * 1.25;
}
if (Random != 0)
{
//generate samples of the Triangular(low, high, mode) distribution;
Triangular.Samples(rnd, sampledata, lowEstimate, highEstimate, mostLikelyEstimate);
}
else
{
//generate samples of the Triangular(low, high, mode) distribution;
Triangular.Samples(sampledata, lowEstimate, highEstimate, mostLikelyEstimate);
}
}
else if (distType == Calculator1.RUC_TYPES.normal.ToString())
{
//generate samples of the Normal(mean, sd) distribution;
if (Random != 0)
{
Normal.Samples(rnd, sampledata, lowEstimate, highEstimate);
}
else
{
Normal.Samples(sampledata, lowEstimate, highEstimate);
}
}
else if (distType == Calculator1.RUC_TYPES.lognormal.ToString())
{
if (Random != 0)
{
LogNormal.Samples(rnd, sampledata, lowEstimate, highEstimate);
}
else
{
LogNormal.Samples(sampledata, lowEstimate, highEstimate);
}
}
else if (distType == Calculator1.RUC_TYPES.weibull.ToString())
{
if (Random != 0)
{
Weibull.Samples(rnd, sampledata, lowEstimate, highEstimate);
}
else
{
Weibull.Samples(sampledata, lowEstimate, highEstimate);
}
}
else if (distType == Calculator1.RUC_TYPES.beta.ToString())
{
if (Random != 0)
{
Beta.Samples(rnd, sampledata, lowEstimate, highEstimate);
}
else
{
Beta.Samples(sampledata, lowEstimate, highEstimate);
}
}
else if (distType == Calculator1.RUC_TYPES.pareto.ToString())
{
if (Random != 0)
{
Pareto.Samples(rnd, sampledata, lowEstimate, highEstimate);
}
else
{
Pareto.Samples(sampledata, lowEstimate, highEstimate);
}
}
else if (distType == Calculator1.RUC_TYPES.uniform.ToString())
{
var sampleints = new int[Iterations];
int iLower = CalculatorHelpers.ConvertStringToInt(lowEstimate.ToString());
int iUpper = CalculatorHelpers.ConvertStringToInt(highEstimate.ToString());
if (Random != 0)
{
DiscreteUniform.Samples(rnd, sampleints, iLower, iUpper);
}
else
{
DiscreteUniform.Samples(sampleints, iLower, iUpper);
}
for (int i = 0; i < sampleints.Count(); i++)
{
sampledata[i] = sampleints[i];
}
}
else if (distType == Calculator1.RUC_TYPES.bernoulli.ToString())
{
var sampleints = new int[Iterations];
if (Random != 0)
{
Bernoulli.Samples(rnd, sampleints, lowEstimate);
}
else
{
Bernoulli.Samples(sampleints, lowEstimate);
}
for (int i = 0; i < sampleints.Count(); i++)
{
sampledata[i] = sampleints[i];
}
}
else if (distType == Calculator1.RUC_TYPES.poisson.ToString())
{
var sampleints = new int[Iterations];
if (Random != 0)
{
Poisson.Samples(rnd, sampleints, lowEstimate);
}
else
{
Poisson.Samples(sampleints, lowEstimate);
}
for (int i = 0; i < sampleints.Count(); i++)
{
sampledata[i] = sampleints[i];
}
}
else if (distType == Calculator1.RUC_TYPES.binomial.ToString())
{
var sampleints = new int[Iterations];
int iUpperEstimate = CalculatorHelpers.ConvertStringToInt(highEstimate.ToString());
if (Random != 0)
{
Binomial.Samples(rnd, sampleints, lowEstimate, iUpperEstimate);
}
else
{
Binomial.Samples(sampleints, lowEstimate, iUpperEstimate);
}
for (int i = 0; i < sampleints.Count(); i++)
{
sampledata[i] = sampleints[i];
}
}
else if (distType == Calculator1.RUC_TYPES.gamma.ToString())
{
//generate samples of the Gamma(shape, scale) distribution;
if (Random != 0)
{
Gamma.Samples(rnd, sampledata, lowEstimate, highEstimate);
}
else
{
Gamma.Samples(sampledata, lowEstimate, highEstimate);
}
}
else
{
//don't force them to use distribution
}
//hold for possible infernet use
//else if (distType == Calculator1.RUC_TYPES.dirichlet.ToString())
//{
// //generate samples of the Dirichlet(random, alpha) distribution;
// Dirichlet.Sample(sampledata, lowEstimate);
//}
//else if (distType == Calculator1.RUC_TYPES.wishart.ToString())
//{
// //generate samples of the Wishart(random, degrees of freedom, scale) distribution;
// Wishart.Sample(sampledata, lowEstimate, highEstimate);
//}
//the mathlibrary supports more than a dozen additional distributions
return(sampledata);
}
/// <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 int[100000];
Poisson.Samples(data, 1);
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.Samples(data, 4);
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.Samples(data, 10);
ConsoleHelper.DisplayHistogram(data);
}
