55 lines
2.0 KiB
C#
55 lines
2.0 KiB
C#
using System;
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using static System.Math;
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namespace Unity.PerformanceTesting.Statistics
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{
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static class NormalDistributionHelper
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{
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/// <summary>
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/// ACM Algorithm 209: Gauss
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///
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/// Calculates $(1/\sqrt{2\pi}) \int_{-\infty}^x e^{-u^2 / 2} du$
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/// by means of polynomial approximations due to A. M. Murray of Aberdeen University;
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///
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/// See: http://dl.acm.org/citation.cfm?id=367664
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/// </summary>
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/// <param name="x">-infinity..+infinity</param>
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/// <returns>Area under the Standard Normal Curve from -infinity to x</returns>
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public static double Gauss(double x)
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{
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double z;
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if (Abs(x) < 1e-9)
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z = 0.0;
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else
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{
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var y = Abs(x) / 2;
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if (y >= 3.0)
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z = 1.0;
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else if (y < 1.0)
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{
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var w = y * y;
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z = ((((((((0.000124818987 * w - 0.001075204047) * w
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+ 0.005198775019) * w - 0.019198292004) * w
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+ 0.059054035642) * w - 0.151968751364) * w
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+ 0.319152932694) * w - 0.531923007300) * w
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+ 0.797884560593) * y * 2.0;
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}
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else
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{
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y = y - 2.0;
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z = (((((((((((((-0.000045255659 * y + 0.000152529290) * y
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- 0.000019538132) * y - 0.000676904986) * y
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+ 0.001390604284) * y - 0.000794620820) * y
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- 0.002034254874) * y + 0.006549791214) * y
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- 0.010557625006) * y + 0.011630447319) * y
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- 0.009279453341) * y + 0.005353579108) * y
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- 0.002141268741) * y + 0.000535310849) * y
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+ 0.999936657524;
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}
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}
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return x > 0.0 ? (z + 1.0) / 2 : (1.0 - z) / 2;
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}
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}
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}
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