/// <summary>Create a specific <see cref="ExponentialDistribution"/> object that represents a specified distribution with estimated parameters.
/// </summary>
/// <param name="empiricalDistribution">The sample to fit the parameters of the specified distribution in its <see cref="EmpiricalDistribution"/> representation.</param>
/// <returns>A specific <see cref="ExponentialDistribution"/> object that represents the specified distribution with estimated parameters.</returns>
public ExponentialDistribution Create(EmpiricalDistribution empiricalDistribution)
{
if (empiricalDistribution.Mean <= 0.0)
{
throw new ArgumentException("empiricalDistribution");
}
var lambda = 1.0 / empiricalDistribution.Mean;
if (InfoOutputDetailLevel.IsAtLeastAsComprehensiveAs(InfoOutputDetailLevel.High) == true)
{
return(new ExponentialDistribution(lambda, (infoOutput, categoryName) =>
{
var infoOutputPackage = infoOutput.AcquirePackage(categoryName);
var dataTable = new DataTable("Sample");
dataTable.Columns.Add("Value", typeof(double));
foreach (var value in empiricalDistribution.Sample)
{
dataTable.Rows.Add(new object[] { value });
}
infoOutputPackage.Add(dataTable);
}));
}
else
{
return(new ExponentialDistribution(lambda));
}
}
/// <summary>Create a specific <see cref="StandardNormalDistribution"/> object that represents a specified distribution with estimated parameters.
/// </summary>
/// <param name="empiricalDistribution">The sample to fit the parameters of the specified distribution in its <see cref="EmpiricalDistribution"/> representation.</param>
/// <returns>A specific <see cref="LogNormalDistribution"/> object that represents the specified distribution with estimated parameters.</returns>
public LogNormalDistribution Create(EmpiricalDistribution empiricalDistribution)
{
var variance = Math.Log(1 + empiricalDistribution.Moment.Variance / (empiricalDistribution.Mean * empiricalDistribution.Mean)); // = ln(1 + sn^2 / \hat{x_n}^2 )
var mu = Math.Log(empiricalDistribution.Mean) - 0.5 * variance; // = ln( \hat{x_n} ) - 0.5 * ln(1 + sn^2 / \hat{x_n}^2 )
if (InfoOutputDetailLevel.IsAtLeastAsComprehensiveAs(InfoOutputDetailLevel.High) == true)
{
return(new LogNormalDistribution(mu, Math.Sqrt(variance), (infoOutput, categoryName) =>
{
var infoOutputPackage = infoOutput.AcquirePackage(categoryName);
var dataTable = new DataTable("Sample");
dataTable.Columns.Add("Value", typeof(double));
foreach (var value in empiricalDistribution.Sample)
{
dataTable.Rows.Add(new object[] { value });
}
infoOutputPackage.Add(dataTable);
}));
}
else
{
return(new LogNormalDistribution(mu, Math.Sqrt(variance)));
}
}
/// <summary>Create a specific <see cref="LogNormalDistribution"/> object that represents a specified distribution with estimated parameters.
/// </summary>
/// <param name="empiricalDistribution">The sample to fit the parameters of the specified distribution in its <see cref="EmpiricalDistribution"/> representation.</param>
/// <returns>A specific <see cref="LogNormalDistribution"/> object that represents the specified distribution with estimated parameters.</returns>
public LogNormalDistribution Create(EmpiricalDistribution empiricalDistribution)
{
var mu = DoMath.Average(empiricalDistribution.Sample.Select(xn => Math.Log(xn)));
var variance = DoMath.Average(empiricalDistribution.Sample.Select(xn => DoMath.Pow(Math.Log(xn) - mu, 2)));
if (InfoOutputDetailLevel.IsAtLeastAsComprehensiveAs(InfoOutputDetailLevel.High) == true)
{
return(new LogNormalDistribution(mu, Math.Sqrt(variance), (infoOutput, categoryName) =>
{
var infoOutputPackage = infoOutput.AcquirePackage(categoryName);
var dataTable = new DataTable("Sample");
dataTable.Columns.Add("Value", typeof(double));
foreach (var value in empiricalDistribution.Sample)
{
dataTable.Rows.Add(new object[] { value });
}
infoOutputPackage.Add(dataTable);
}));
}
else
{
return(new LogNormalDistribution(mu, Math.Sqrt(variance)));
}
}
/// <summary>Create a specific <see cref="NormalDistribution"/> object that represents a specified distribution with estimated parameters.
/// </summary>
/// <param name="empiricalDistribution">The sample to fit the parameters of the specified distribution in its <see cref="EmpiricalDistribution"/> representation.</param>
/// <returns>A specific <see cref="NormalDistribution"/> object that represents the specified distribution with estimated parameters.</returns>
public NormalDistribution Create(EmpiricalDistribution empiricalDistribution)
{
var mu = empiricalDistribution.Mean;
var sigma = empiricalDistribution.Moment.StandardDeviation;
if (InfoOutputDetailLevel.IsAtLeastAsComprehensiveAs(InfoOutputDetailLevel.High) == true)
{
return(new NormalDistribution(mu, sigma, (infoOutput, categoryName) =>
{
var infoOutputPackage = infoOutput.AcquirePackage(categoryName);
var dataTable = new DataTable("Sample");
dataTable.Columns.Add("Value", typeof(double));
foreach (var value in empiricalDistribution.Sample)
{
dataTable.Rows.Add(new object[] { value });
}
infoOutputPackage.Add(dataTable);
}));
}
else
{
return(new NormalDistribution(mu, sigma));
}
}
/// <summary>Create a specific <see cref="NormalDistribution"/> object that represents a specified distribution with estimated parameters.
/// </summary>
/// <param name="empiricalDistribution">The sample to fit the parameters of the specified distribution in its <see cref="EmpiricalDistribution"/> representation.</param>
/// <returns>A specific <see cref="NormalDistribution"/> object that represents the specified distribution with estimated parameters.</returns>
public NormalDistribution Create(EmpiricalDistribution empiricalDistribution)
{
var n = empiricalDistribution.SampleSize;
var mu = empiricalDistribution.Mean;
var sigma = Math.Sqrt(empiricalDistribution.Moment.Variance * (n - 1.0) / n); // apply 1/n instead of 1/(n-1.0) in the estimator of the variance
if (InfoOutputDetailLevel.IsAtLeastAsComprehensiveAs(InfoOutputDetailLevel.High) == true)
{
return(new NormalDistribution(mu, sigma, (infoOutput, categoryName) =>
{
var infoOutputPackage = infoOutput.AcquirePackage(categoryName);
var dataTable = new DataTable("Sample");
dataTable.Columns.Add("Value", typeof(double));
foreach (var value in empiricalDistribution.Sample)
{
dataTable.Rows.Add(new object[] { value });
}
infoOutputPackage.Add(dataTable);
}));
}
else
{
return(new NormalDistribution(mu, sigma));
}
}
/// <summary>Initializes a new instance of the <see cref="EmpiricalDistribution" /> class.
/// </summary>
/// <param name="empiricalDistribution">The empirical distribution.</param>
/// <param name="densityEstimator">The density estimator.</param>
protected EmpiricalDistribution(EmpiricalDistribution empiricalDistribution, DensityEstimator densityEstimator)
{
m_Median = empiricalDistribution.m_Median;
m_Quantile = empiricalDistribution.m_Quantile;
m_MomentCalculator = empiricalDistribution.m_MomentCalculator;
Name = empiricalDistribution.Name;
LongName = empiricalDistribution.LongName;
m_DensityEstimator = densityEstimator.Create(this);
InfoOutputDetailLevel = empiricalDistribution.InfoOutputDetailLevel;
}
/// <summary>Gets an unbiased covariance estimator of two random samples.
/// </summary>
/// <param name="sample1">The first sample.</param>
/// <param name="sample2">The second sample.</param>
/// <returns>The estimated covariance of the two specified samples.</returns>
/// <remarks>The implementation is based on "Formulas for Robust, One-pass parallel computation of Covariances and arbitrary-order statistic Moments", P. Pebay, Sandia National Laboratories, September 2008.</remarks>
public static double GetCovariance(EmpiricalDistribution sample1, EmpiricalDistribution sample2)
{
var c2 = 0.0;
var mean1 = 0.0;
var mean2 = 0.0;
var sample2Enumerator = sample2.Sample.GetEnumerator();
int n = 1;
foreach (var value1 in sample1.Sample)
{
sample2Enumerator.MoveNext();
var value2 = sample2Enumerator.Current;
c2 += (value1 - mean1) * (value2 - mean2) * (n - 1) / n;
mean1 += (value1 - mean1) / n;
mean2 += (value2 - mean2) / n;
n++;
}
return(c2 / (n - 2)); // n is sample length + 1 at this time
}
/// <summary>Gets the estimated Pearson's correlation coefficient of two samples.
/// </summary>
/// <param name="sample1">The first sample.</param>
/// <param name="sample2">The second sample.</param>
/// <returns>The estimated Pearson's correlation coefficient, i.e. the covariance of the two specified samples divided by the product of their standard deviations.</returns>
/// <remarks>The implementation is based on "Formulas for Robust, One-pass parallel computation of Covariances and arbitrary-order statistic Moments", P. Pebay, Sandia National Laboratories, September 2008.</remarks>
public static double GetCorrelationCoefficient(EmpiricalDistribution sample1, EmpiricalDistribution sample2)
{
return(GetCovariance(sample1, sample2) / (sample1.Moment.StandardDeviation * sample2.Moment.StandardDeviation));
}
