public void ValidateCumulativeDistribution(double lambda, double x)
{
var n = new Exponential(lambda);
if (x >= 0.0)
{
Assert.AreEqual <double>(1.0 - Math.Exp(-lambda * x), n.CumulativeDistribution(x));
}
else
{
Assert.AreEqual <double>(0.0, n.CumulativeDistribution(x));
}
}
public void ValidateCumulativeDistribution(
[Values(0.0, 0.1, 1.0, 10.0, Double.PositiveInfinity, 0.0, 0.1, 1.0, 10.0, Double.PositiveInfinity, 0.0, 0.1, 1.0, 10.0, Double.PositiveInfinity, 0.0, 0.1, 1.0, 10.0, Double.PositiveInfinity)] double lambda,
[Values(0.0, 0.0, 0.0, 0.0, 0.0, 0.1, 0.1, 0.1, 0.1, 0.1, 1.0, 1.0, 1.0, 1.0, 1.0, Double.PositiveInfinity, Double.PositiveInfinity, Double.PositiveInfinity, Double.PositiveInfinity, Double.PositiveInfinity)] double x)
{
var n = new Exponential(lambda);
if (x >= 0.0)
{
Assert.AreEqual(1.0 - Math.Exp(-lambda * x), n.CumulativeDistribution(x));
}
else
{
Assert.AreEqual(0.0, n.CumulativeDistribution(x));
}
}
public double CumulativeProbability(Position1 sample)
{
if (sample <= Domain.Entry)
{
return(0);
}
else if (sample <= Domain.Exit)
{
return(distribution.CumulativeDistribution(((float)sample).Previous() - Domain.Entry));
}
else
{
return(distribution.CumulativeDistribution(Domain.CoveredArea));
}
}
/// <summary>
/// Run example
/// </summary>
/// <a href="http://en.wikipedia.org/wiki/Exponential_distribution">Exponential distribution</a>
public void Run()
{
// 1. Initialize the new instance of the Exponential distribution class with parameter Lambda = 1.
var exponential = new Exponential(1);
Console.WriteLine(@"1. Initialize the new instance of the Exponential distribution class with parameter Lambda = {0}", exponential.Rate);
Console.WriteLine();
// 2. Distributuion properties:
Console.WriteLine(@"2. {0} distributuion properties:", exponential);
// Cumulative distribution function
Console.WriteLine(@"{0} - Сumulative distribution at location '0.3'", exponential.CumulativeDistribution(0.3).ToString(" #0.00000;-#0.00000"));
// Probability density
Console.WriteLine(@"{0} - Probability density at location '0.3'", exponential.Density(0.3).ToString(" #0.00000;-#0.00000"));
// Log probability density
Console.WriteLine(@"{0} - Log probability density at location '0.3'", exponential.DensityLn(0.3).ToString(" #0.00000;-#0.00000"));
// Entropy
Console.WriteLine(@"{0} - Entropy", exponential.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
Console.WriteLine(@"{0} - Largest element in the domain", exponential.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
Console.WriteLine(@"{0} - Smallest element in the domain", exponential.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
Console.WriteLine(@"{0} - Mean", exponential.Mean.ToString(" #0.00000;-#0.00000"));
// Median
Console.WriteLine(@"{0} - Median", exponential.Median.ToString(" #0.00000;-#0.00000"));
// Mode
Console.WriteLine(@"{0} - Mode", exponential.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
Console.WriteLine(@"{0} - Variance", exponential.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
Console.WriteLine(@"{0} - Standard deviation", exponential.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
Console.WriteLine(@"{0} - Skewness", exponential.Skewness.ToString(" #0.00000;-#0.00000"));
Console.WriteLine();
// 3. Generate 10 samples of the Exponential distribution
Console.WriteLine(@"3. Generate 10 samples of the Exponential distribution");
for (var i = 0; i < 10; i++)
{
Console.Write(exponential.Sample().ToString("N05") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 4. Generate 100000 samples of the Exponential(1) distribution and display histogram
Console.WriteLine(@"4. Generate 100000 samples of the Exponential(1) distribution and display histogram");
var data = new double[100000];
for (var i = 0; i < data.Length; i++)
{
data[i] = exponential.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 5. Generate 100000 samples of the Exponential(9) distribution and display histogram
Console.WriteLine(@"5. Generate 100000 samples of the Exponential(9) distribution and display histogram");
exponential.Rate = 9;
for (var i = 0; i < data.Length; i++)
{
data[i] = exponential.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 6. Generate 100000 samples of the Exponential(0.01) distribution and display histogram
Console.WriteLine(@"6. Generate 100000 samples of the Exponential(0.01) distribution and display histogram");
exponential.Rate = 0.01;
for (var i = 0; i < data.Length; i++)
{
data[i] = exponential.Sample();
}
ConsoleHelper.DisplayHistogram(data);
}
public void ValidateCumulativeDistribution(double lambda, double x)
{
var n = new Exponential(lambda);
if (x >= 0.0)
{
Assert.AreEqual(1.0 - Math.Exp(-lambda * x), n.CumulativeDistribution(x));
}
else
{
Assert.AreEqual(0.0, n.CumulativeDistribution(x));
}
}
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;
}
}
public void ValidateCumulativeDistribution(
[Values(0.0, 0.1, 1.0, 10.0, Double.PositiveInfinity, 0.0, 0.1, 1.0, 10.0, Double.PositiveInfinity, 0.0, 0.1, 1.0, 10.0, Double.PositiveInfinity, 0.0, 0.1, 1.0, 10.0, Double.PositiveInfinity)] double lambda,
[Values(0.0, 0.0, 0.0, 0.0, 0.0, 0.1, 0.1, 0.1, 0.1, 0.1, 1.0, 1.0, 1.0, 1.0, 1.0, Double.PositiveInfinity, Double.PositiveInfinity, Double.PositiveInfinity, Double.PositiveInfinity, Double.PositiveInfinity)] double x)
{
var n = new Exponential(lambda);
if (x >= 0.0)
{
Assert.AreEqual(1.0 - Math.Exp(-lambda * x), n.CumulativeDistribution(x));
}
else
{
Assert.AreEqual(0.0, n.CumulativeDistribution(x));
}
}
