/// <summary>
/// Generates a random observation from the
/// Cauchy distribution with the given parameters.
/// </summary>
///
/// <param name="location">The location parameter x0.</param>
/// <param name="scale">The scale parameter gamma.</param>
/// <param name="source">The random number generator to use as a source of randomness.
/// Default is to use <see cref="Accord.Math.Random.Generator.Random"/>.</param>
///
/// <returns>A random double value sampled from the specified Cauchy distribution.</returns>
///
public static double Random(double location, double scale, Random source)
{
// Generate uniform U on [-PI/2, +PI/2]
double x = UniformContinuousDistribution.Random(-Math.PI / 2.0, +Math.PI / 2.0, source);
return(Math.Tan(x) * scale + location);
}
/// <summary>
/// Estimates a new uniform distribution from a given set of observations.
/// </summary>
///
public static UniformContinuousDistribution Estimate(double[] observations)
{
var n = new UniformContinuousDistribution();
n.Fit(observations, null, null);
return(n);
}
/// <summary>
/// Generates a random vector of observations from the current distribution.
/// </summary>
///
/// <param name="samples">The number of samples to generate.</param>
/// <param name="result">The location where to store the samples.</param>
///
/// <returns>A random vector of observations drawn from this distribution.</returns>
///
public override double[] Generate(int samples, double[] result)
{
UniformContinuousDistribution.Random(samples, result);
for (int i = 0; i < samples; i++)
{
result[i] = xm / Math.Pow(result[i], 1.0 / alpha);
}
return(result);
}
/// <summary>
/// Generates a random observation from the current distribution.
/// </summary>
///
/// <returns>A random observations drawn from this distribution.</returns>
///
public override double Generate(Random source)
{
double u = UniformContinuousDistribution.Random(source);
double Fc = DistributionFunction(c);
if (u < Fc)
return a + Math.Sqrt(u * (b - a) * (c - a));
return b - Math.Sqrt((1 - u) * (b - a) * (b - c));
}
/// <summary>
/// Generates a random vector of observations from the
/// Cauchy distribution with the given parameters.
/// </summary>
///
/// <param name="location">The location parameter x0.</param>
/// <param name="scale">The scale parameter gamma.</param>
/// <param name="samples">The number of samples to generate.</param>
/// <param name="result">The location where to store the samples.</param>
/// <param name="source">The random number generator to use as a source of randomness.
/// Default is to use <see cref="Accord.Math.Random.Generator.Random"/>.</param>
///
/// <returns>An array of double values sampled from the specified Cauchy distribution.</returns>
///
public static double[] Random(double location, double scale, int samples, double[] result, Random source)
{
// Generate uniform U on [-PI/2, +PI/2]
UniformContinuousDistribution.Random(-Math.PI / 2.0, +Math.PI / 2.0, samples, result, source);
for (int i = 0; i < result.Length; i++)
{
result[i] = Math.Tan(result[i]) * scale + location;
}
return(result);
}
/// <summary>
/// Generates a random vector of observations from the
/// Cauchy distribution with the given parameters.
/// </summary>
///
/// <param name="location">The location parameter x0.</param>
/// <param name="scale">The scale parameter gamma.</param>
/// <param name="samples">The number of samples to generate.</param>
///
/// <returns>An array of double values sampled from the specified Cauchy distribution.</returns>
///
public static double[] Random(double location, double scale, int samples)
{
// Generate uniform U on [-PI/2, +PI/2]
double[] x = UniformContinuousDistribution.Random(-Math.PI / 2.0, +Math.PI / 2.0, samples);
for (int i = 0; i < x.Length; i++)
{
x[i] = Math.Tan(x[i]) * scale + location;
}
return(x);
}
/// <summary>
/// Generates a random observation from the current distribution.
/// </summary>
///
/// <param name="source">The random number generator to use as a source of randomness.
/// Default is to use <see cref="Accord.Math.Random.Generator.Random"/>.</param>
///
/// <returns>A random observations drawn from this distribution.</returns>
///
public override double Generate(Random source)
{
double U = UniformContinuousDistribution.Random(source);
if (ksi == 0)
{
return(mu - sigma * Math.Log(U));
}
return(mu + sigma * (Math.Pow(U, -ksi) - 1) / ksi);
}
/// <summary>
/// Generates a random observation from the current distribution.
/// </summary>
///
/// <returns>A random observations drawn from this distribution.</returns>
///
public override double Generate()
{
double u = UniformContinuousDistribution.Random();
double Fc = DistributionFunction(c);
if (u < Fc)
{
return(a + Math.Sqrt(u * (b - a) * (c - a)));
}
return(b - Math.Sqrt((1 - u) * (b - a) * (b - c)));
}
/// <summary>
/// Generates a random vector of observations from the current distribution.
/// </summary>
///
/// <param name="samples">The number of samples to generate.</param>
/// <param name="result">The location where to store the samples.</param>
/// <param name="source">The random number generator to use as a source of randomness.
/// Default is to use <see cref="Accord.Math.Random.Generator.Random"/>.</param>
///
/// <returns>A random vector of observations drawn from this distribution.</returns>
///
public override double[] Generate(int samples, double[] result, Random source)
{
double Fc = DistributionFunction(c);
UniformContinuousDistribution.Random(samples, result, source);
for (int i = 0; i < samples; i++)
{
double u = result[i];
if (u < Fc)
result[i] = a + Math.Sqrt(u * (b - a) * (c - a));
else
result[i] = b - Math.Sqrt((1 - u) * (b - a) * (b - c));
}
return result;
}
/// <summary>
/// Generates a random vector of observations from the current distribution.
/// </summary>
///
/// <param name="samples">The number of samples to generate.</param>
/// <returns>A random vector of observations drawn from this distribution.</returns>
///
public double[] Generate(int samples)
{
double Fc = DistributionFunction(c);
double[] values = UniformContinuousDistribution.Random(samples);
for (int i = 0; i < values.Length; i++)
{
double u = values[i];
if (u < Fc)
{
values[i] = a + Math.Sqrt(u * (b - a) * (c - a));
}
values[i] = b - Math.Sqrt((1 - u) * (b - a) * (b - c));
}
return(values);
}
/// <summary>
/// Generates a random vector of observations from the current distribution.
/// </summary>
///
/// <param name="samples">The number of samples to generate.</param>
/// <param name="result">The location where to store the samples.</param>
/// <param name="source">The random number generator to use as a source of randomness.
/// Default is to use <see cref="Accord.Math.Random.Generator.Random"/>.</param>
///
/// <returns>A random vector of observations drawn from this distribution.</returns>
///
public override double[] Generate(int samples, double[] result, Random source)
{
UniformContinuousDistribution.Random(samples, result, source);
if (ksi == 0)
{
for (int i = 0; i < result.Length; i++)
{
result[i] = mu - sigma * Math.Log(result[i]);
}
}
else
{
for (int i = 0; i < result.Length; i++)
{
result[i] = mu + sigma * (Math.Pow(result[i], -ksi) - 1) / ksi;
}
}
return(result);
}
/// <summary>
/// Generates a random observation from the current distribution.
/// </summary>
///
/// <returns>A random observations drawn from this distribution.</returns>
///
public override double Generate(Random source)
{
double u = UniformContinuousDistribution.Random(source);
return(xm / Math.Pow(u, 1.0 / alpha));
}