/// <summary>
/// Samples Beta distributed random variables by sampling two Gamma variables and normalizing.
/// </summary>
/// <param name="rnd">The random number generator to use.</param>
/// <param name="a">The α shape parameter of the Beta distribution. Range: α ≥ 0.</param>
/// <param name="b">The β shape parameter of the Beta distribution. Range: β ≥ 0.</param>
/// <returns>a random number from the Beta distribution.</returns>
internal static double SampleUnchecked(System.Random rnd, double a, double b)
{
var x = Gamma.SampleUnchecked(rnd, a, 1.0);
var y = Gamma.SampleUnchecked(rnd, b, 1.0);
return(x / (x + y));
}
/// <summary>
/// Generates a sequence of samples from the Erlang distribution.
/// </summary>
/// <returns>a sequence of samples from the distribution.</returns>
public IEnumerable <double> Samples()
{
while (true)
{
yield return(Gamma.SampleUnchecked(_random, _shape, _rate));
}
}
/// <summary>
/// Samples a negative binomial distributed random variable.
/// </summary>
/// <param name="rnd">The random number generator to use.</param>
/// <param name="r">The number of successes (r) required to stop the experiment. Range: r ≥ 0.</param>
/// <param name="p">The probability (p) of a trial resulting in success. Range: 0 ≤ p ≤ 1.</param>
/// <returns>a sample from the distribution.</returns>
static int SampleUnchecked(System.Random rnd, double r, double p)
{
var lambda = Gamma.SampleUnchecked(rnd, r, p);
var c = Math.Exp(-lambda);
var p1 = 1.0;
var k = 0;
do
{
k = k + 1;
p1 = p1 * rnd.NextDouble();
}while (p1 >= c);
return(k - 1);
}
/// <summary>
/// Samples the distribution.
/// </summary>
/// <param name="rnd">The random number generator to use.</param>
/// <param name="freedom">The degrees of freedom (k) of the distribution. Range: k > 0.</param>
/// <returns>a random number from the distribution.</returns>
static double SampleUnchecked(System.Random rnd, double freedom)
{
// Use the simple method if the degrees of freedom is an integer anyway
if (Math.Floor(freedom) == freedom && freedom < int.MaxValue)
{
double sum = 0;
var n = (int)freedom;
for (var i = 0; i < n; i++)
{
sum += Math.Pow(Normal.Sample(rnd, 0.0, 1.0), 2);
}
return(sum);
}
// Call the gamma function (see http://en.wikipedia.org/wiki/Gamma_distribution#Specializations
// for a justification)
return(Gamma.SampleUnchecked(rnd, freedom / 2.0, .5));
}
static double SampleUnchecked(System.Random rnd, double shape, double scale)
{
return(1.0 / Gamma.SampleUnchecked(rnd, shape, scale));
}
/// <summary>
/// Samples 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="location">The location (μ) of the distribution.</param>
/// <param name="scale">The scale (σ) of the distribution. Range: σ > 0.</param>
/// <param name="freedom">The degrees of freedom (ν) for the distribution. Range: ν > 0.</param>
/// <returns>a random number from the standard student-t distribution.</returns>
static double SampleUnchecked(System.Random rnd, double location, double scale, double freedom)
{
var gamma = Gamma.SampleUnchecked(rnd, 0.5 * freedom, 0.5);
return(Normal.Sample(rnd, location, scale * Math.Sqrt(freedom / gamma)));
}
/// <summary>
/// Generates a sample from the Erlang distribution.
/// </summary>
/// <returns>a sample from the distribution.</returns>
public double Sample()
{
return(Gamma.SampleUnchecked(_random, _shape, _rate));
}
