private void fitMLE(double sum1, double sum2, double n)
{
double[] gradient = new double[2];
var bfgs = new BoundedBroydenFletcherGoldfarbShanno(numberOfVariables: 2);
bfgs.LowerBounds[0] = 1e-100;
bfgs.LowerBounds[1] = 1e-100;
bfgs.Solution[0] = this.alpha;
bfgs.Solution[1] = this.beta;
bfgs.Function = (double[] parameters) =>
BetaDistribution.LogLikelihood(sum1, sum2, n, parameters[0], parameters[1]);
bfgs.Gradient = (double[] parameters) =>
BetaDistribution.Gradient(sum1, sum2, n, parameters[0], parameters[1], gradient);
if (!bfgs.Minimize())
{
throw new ConvergenceException();
}
this.alpha = bfgs.Solution[0];
this.beta = bfgs.Solution[1];
}
/// <summary>
/// Estimates a new Beta distribution from a set of observations.
/// </summary>
///
public static BetaDistribution Estimate(double[] samples, BetaOptions options)
{
var beta = new BetaDistribution(1, 1);
beta.Fit(samples, (double[])null, options);
return(beta);
}
/// <summary>
/// Estimates a new Beta distribution from a set of weighted observations.
/// </summary>
///
public static BetaDistribution Estimate(double[] samples, double[] weights)
{
var beta = new BetaDistribution(1, 1);
beta.Fit(samples, weights, null);
return(beta);
}
/// <summary>
/// Generates a random vector of observations from the
/// Beta distribution with the given parameters.
/// </summary>
///
/// <param name="alpha">The shape parameter α (alpha).</param>
/// <param name="beta">The shape parameter β (beta).</param>
/// <param name="min">The minimum possible value a.</param>
/// <param name="max">The maximum possible value b.</param>
/// <param name="samples">The number of samples to generate.</param>
///
/// <returns>An array of double values sampled from the specified Beta distribution.</returns>
///
public static double[] Random(double alpha, double beta, double min, double max, int samples)
{
double[] r = BetaDistribution.Random(alpha, beta, samples);
if (min != 0 || max != 1)
{
for (int i = 0; i < r.Length; i++)
{
r[i] = r[i] * (max - min) + min;
}
}
return(r);
}
/// <summary>
/// Generates a random observation from a
/// Beta distribution with the given parameters.
/// </summary>
///
/// <param name="alpha">The shape parameter α (alpha).</param>
/// <param name="beta">The shape parameter β (beta).</param>
/// <param name="min">The minimum possible value a.</param>
/// <param name="max">The maximum possible value b.</param>
///
/// <returns>A random double value sampled from the specified Beta distribution.</returns>
///
public static double Random(double alpha, double beta, double min, double max)
{
double r = BetaDistribution.Random(alpha, beta);
return(r * (max - min) + min);
}