97 lines
4.8 KiB
C#
97 lines
4.8 KiB
C#
using System;
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using System.Collections.Generic;
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using System.Linq;
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using System.Text;
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using BotSharp.Algorithm.HiddenMarkovModel.MathUtils.Distribution;
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namespace BotSharp.Algorithm.HiddenMarkovModel.MathUtils.Statistics
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{
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/// <summary>
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/// Statistics related to the linear combination of two variables.
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/// </summary>
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public class LinearCombination
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{
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/// <summary>
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/// Return the distribution of a*x + b*y for correlated random variables x and y
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/// </summary>
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/// <param name="x">random variable x</param>
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/// <param name="y">random variable y</param>
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/// <param name="x_coefficient">a which is the coefficient of x</param>
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/// <param name="y_coefficient">b which is the coefficient of y</param>
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/// <param name="correlation">correlation between x and y</param>
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/// <returns></returns>
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public static DistributionModel Sum(DistributionModel x, DistributionModel y, int x_coefficient, double y_coefficient, double correlation)
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{
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DistributionModel sum = x.Clone();
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sum.Mean = x_coefficient * x.Mean + y_coefficient * y.Mean;
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sum.StdDev = System.Math.Sqrt(System.Math.Pow(x_coefficient * x.StdDev, 2) + System.Math.Pow(y_coefficient * y.StdDev, 2) + 2 * correlation * x_coefficient * x.StdDev * y_coefficient * y.StdDev);
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return sum;
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}
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/// <summary>
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/// Return the NormalTable distribution of population statistic (a*x + b*y) for correlated random variables x and y
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/// </summary>
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/// <param name="x">random sample for random variable x</param>
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/// <param name="y">random sample for random variable y</param>
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/// <param name="x_coefficient">a which is the coefficient of x</param>
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/// <param name="y_coefficient">b which is the coefficient of y</param>
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/// <param name="correlation">correlation between x and y</param>
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/// <param name="result_mean">output mean for the a*x + b*y</param>
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/// <param name="result_SE">output standard error for the a*x + b*y</param>
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public static void Sum(double[] x, double[] y, int x_coefficient, double y_coefficient, double correlation, out double result_mean, out double result_SE)
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{
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result_mean = 0;
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result_SE = 0;
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double mean_x = Mean.GetMean(x);
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double mean_y = Mean.GetMean(y);
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double stddev_x = StdDev.GetStdDev(x, mean_x);
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double stddev_y = StdDev.GetStdDev(y, mean_y);
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result_mean = x_coefficient * mean_x + y_coefficient * mean_y;
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result_SE = System.Math.Sqrt(System.Math.Pow(x_coefficient * stddev_x, 2) / x.Length + System.Math.Pow(y_coefficient * stddev_y, 2) / y.Length + 2 * correlation * x_coefficient * stddev_x * y_coefficient * stddev_y / System.Math.Sqrt(x.Length * y.Length));
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}
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/// <summary>
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/// Return the distribution of x + y for correlated random variables x and y
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/// </summary>
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/// <param name="x">random variable x</param>
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/// <param name="y">random variable y</param>
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/// <param name="correlation">correlation between x and y</param>
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/// <returns></returns>
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public static DistributionModel Sum(DistributionModel x, DistributionModel y, double correlation)
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{
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return Sum(x, y, 1, 1, correlation);
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}
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/// <summary>
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/// Return the distribution of x - y for correlated random variables x and y
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/// </summary>
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/// <param name="x">random variable x</param>
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/// <param name="y">random variable y</param>
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/// <param name="correlation">correlation between x and y</param>
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/// <returns></returns>
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public static DistributionModel Diff(DistributionModel x, DistributionModel y, double correlation)
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{
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return Sum(x, y, 1, -1, correlation);
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}
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/// <summary>
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/// Return the NormalTable distribution of population statistic (x - y) for correlated random variables x and y
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/// </summary>
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/// <param name="x">random sample for random variable x</param>
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/// <param name="y">random sample for random variable y</param>
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/// <param name="x_coefficient">a which is the coefficient of x</param>
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/// <param name="y_coefficient">b which is the coefficient of y</param>
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/// <param name="correlation">correlation between x and y</param>
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/// <param name="result_mean">output mean for the a*x + b*y</param>
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/// <param name="result_SE">output standard deviation for the a*x + b*y</param>
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public static void Diff(double[] x, double[] y, double correlation, out double result_mean, out double result_stddev)
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{
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Sum(x, y, 1, -1, correlation, out result_mean, out result_stddev);
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}
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}
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}
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