/// <summary>
/// Generates a random vector of observations from the
/// Inverse Gaussian distribution with the given parameters.
/// </summary>
///
/// <param name="mean">The mean parameter mu.</param>
/// <param name="shape">The shape parameter lambda.</param>
/// <param name="samples">The number of samples to generate.</param>
/// <param name="result">The location where to store the samples.</param>
///
/// <returns>An array of double values sampled from the inverse Gaussian distribution.</returns>
///
public static double[] Random(double mean, double shape, int samples, double[] result)
{
var u = Accord.Math.Random.Generator.Random;
NormalDistribution.Random(samples, result);
for (int i = 0; i < result.Length; i++)
{
double v = result[i];
double y = v * v;
double x = mean + (mean * mean * y) / (2 * shape) - (mean / (2 * shape)) * Math.Sqrt(4 * mean * shape * y + mean * mean * y * y);
double t = u.NextDouble();
if (t <= (mean) / (mean + x))
{
result[i] = x;
}
else
{
result[i] = (mean * mean) / x;
}
}
return(result);
}
/// <summary>
/// Generates a random vector of observations from the
/// Lognormal distribution with the given parameters.
/// </summary>
///
/// <param name="location">The distribution's location value.</param>
/// <param name="shape">The distribution's shape deviation.</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 Lognormal distribution.</returns>
///
public static double[] Random(double location, double shape, int samples, double[] result, Random source)
{
NormalDistribution.Random(samples, result, source);
for (int i = 0; i < result.Length; i++)
{
result[i] = Math.Exp(location + shape * result[i]);
}
return(result);
}
/// <summary>
/// Generates a random observation from the
/// Inverse Gaussian distribution with the given parameters.
/// </summary>
///
/// <param name="mean">The mean parameter mu.</param>
/// <param name="shape">The shape parameter lambda.</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 Uniform distribution.</returns>
///
public static double Random(double mean, double shape, Random source)
{
double v = NormalDistribution.Random(source);
double y = v * v;
double x = mean + (mean * mean * y) / (2 * shape) - (mean / (2 * shape)) * Math.Sqrt(4 * mean * shape * y + mean * mean * y * y);
double t = source.NextDouble();
if (t <= (mean) / (mean + x))
{
return(x);
}
return((mean * mean) / x);
}
/// <summary>
/// Generates a random observation from the
/// Inverse Gaussian distribution with the given parameters.
/// </summary>
///
/// <param name="mean">The mean parameter mu.</param>
/// <param name="shape">The shape parameter lambda.</param>
///
/// <returns>A random double value sampled from the specified Uniform distribution.</returns>
///
public static double Random(double mean, double shape)
{
var u = Accord.Math.Random.Generator.Random;
double v = NormalDistribution.Random();
double y = v * v;
double x = mean + (mean * mean * y) / (2 * shape) - (mean / (2 * shape)) * Math.Sqrt(4 * mean * shape * y + mean * mean * y * y);
double t = u.NextDouble();
if (t <= (mean) / (mean + x))
{
return(x);
}
return((mean * mean) / x);
}
/// <summary>
/// Random Gamma-distribution number generation
/// based on Marsaglia's Simple Method (2000).
/// </summary>
///
public static double Marsaglia(double d, double c)
{
var rand = Accord.Math.Random.Generator.Random;
// References:
//
// - Marsaglia, G. A Simple Method for Generating Gamma Variables, 2000
//
while (true)
{
// 2. Generate v = (1+cx)^3 with x normal
double x, t, v;
do
{
x = NormalDistribution.Random();
t = (1.0 + c * x);
v = t * t * t;
} while (v <= 0);
// 3. Generate uniform U
double U = rand.NextDouble();
// 4. If U < 1-0.0331*x^4 return d*v.
double x2 = x * x;
if (U < 1 - 0.0331 * x2 * x2)
{
return(d * v);
}
// 5. If log(U) < 0.5*x^2 + d*(1-v+log(v)) return d*v.
if (Math.Log(U) < 0.5 * x2 + d * (1.0 - v + Math.Log(v)))
{
return(d * v);
}
// 6. Goto step 2
}
}
/// <summary>
/// Generates a random observation from the
/// Lognormal distribution with the given parameters.
/// </summary>
///
/// <param name="location">The distribution's location value.</param>
/// <param name="shape">The distribution's shape deviation.</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 Lognormal distribution.</returns>
///
public static double Random(double location, double shape, Random source)
{
return(Math.Exp(location + shape * NormalDistribution.Random(source)));
}