/// <summary>
/// Samples standard student-t distributed random variables.
/// </summary>
/// <remarks>The algorithm is method 2 in section 5, chapter 9
/// in L. Devroye's "Non-Uniform Random Variate Generation"</remarks>
/// <param name="rnd">The random number generator to use.</param>
/// <param name="dof">The degrees of freedom for the standard student-t distribution.</param>
/// <returns>a random number from the standard student-t distribution.</returns>
internal static double Sample(Random rnd, double dof)
{
var n = Normal.SampleBoxMuller(rnd).Item1;
var g = Gamma.Sample(rnd, 0.5 * dof, 0.5);
return(Math.Sqrt(dof / g) * n);
}
/// <summary>
/// Generates a sample from the log-normal distribution using the <i>Box-Muller</i> algorithm.
/// </summary>
/// <param name="rng">The random number generator to use.</param>
/// <param name="mu">The mu of the logarithm of the distribution.</param>
/// <param name="sigma">The standard deviation of the logarithm of the distribution.</param>
/// <returns>a sample from the distribution.</returns>
public static double Sample(Random rng, double mu, double sigma)
{
if (Control.CheckDistributionParameters && !IsValidParameterSet(mu, sigma))
{
throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
}
return(Math.Exp(mu + (sigma * Normal.SampleBoxMuller(rng).Item1)));
}
/// <summary>
/// Generates a sequence of samples from the log-normal distribution using the <i>Box-Muller</i> algorithm.
/// </summary>
/// <returns>a sequence of samples from the distribution.</returns>
public IEnumerable <double> Samples()
{
while (true)
{
var sample = Normal.SampleBoxMuller(RandomSource);
yield return(Math.Exp(_mu + (_sigma * sample.Item1)));
yield return(Math.Exp(_mu + (_sigma * sample.Item2)));
}
}
/// <summary>
/// Generates a sequence of samples from the log-normal distribution using the <i>Box-Muller</i> algorithm.
/// </summary>
/// <param name="rng">The random number generator to use.</param>
/// <param name="mu">The mu of the logarithm of the distribution.</param>
/// <param name="sigma">The standard deviation of the logarithm of the distribution.</param>
/// <returns>a sequence of samples from the distribution.</returns>
public static IEnumerable <double> Samples(Random rng, double mu, double sigma)
{
if (Control.CheckDistributionParameters && !IsValidParameterSet(mu, sigma))
{
throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
}
while (true)
{
var sample = Normal.SampleBoxMuller(rng);
yield return(Math.Exp(mu + (sigma * sample.Item1)));
yield return(Math.Exp(mu + (sigma * sample.Item2)));
}
}
/// <summary>
/// Samples a vector normal distributed random variable.
/// </summary>
/// <param name="rnd">The random number generator to use.</param>
/// <param name="mean">The mean of the vector normal distribution.</param>
/// <param name="cholesky">The Cholesky factorization of the covariance matrix.</param>
/// <returns>a sequence of samples from defined distribution.</returns>
private static Vector <double> SampleVectorNormal(Random rnd, Vector <double> mean, Cholesky <double> cholesky)
{
var count = mean.Count;
// Sample a standard normal variable.
var v = new DenseVector(count, 0.0);
for (var d = 0; d < count; d += 2)
{
var sample = Normal.SampleBoxMuller(rnd);
v[d] = sample.Item1;
if (d + 1 < count)
{
v[d + 1] = sample.Item2;
}
}
// Return the transformed variable.
return(mean + (cholesky.Factor * v));
}
/// <summary>
/// Generates a sample from the log-normal distribution using the <i>Box-Muller</i> algorithm.
/// </summary>
/// <returns>a sample from the distribution.</returns>
public double Sample()
{
return(Math.Exp(_mu + (_sigma * Normal.SampleBoxMuller(RandomSource).Item1)));
}
