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518 lines
17 KiB
518 lines
17 KiB
// <copyright file="NormalTests.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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// http://mathnetnumerics.codeplex.com
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// Copyright (c) 2009-2010 Math.NET
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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using System;
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using System.Linq;
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using MathNet.Numerics.Distributions;
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using NUnit.Framework;
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namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
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{
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using Random = System.Random;
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/// <summary>
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/// Normal distribution tests.
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/// </summary>
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[TestFixture]
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public class NormalTests
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{
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/// <summary>
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/// Set-up parameters.
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/// </summary>
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[SetUp]
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public void SetUp()
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{
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Control.CheckDistributionParameters = true;
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}
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/// <summary>
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/// Can create standard normal.
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/// </summary>
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[Test]
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public void CanCreateStandardNormal()
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{
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var n = new Normal();
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Assert.AreEqual(0.0, n.Mean);
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Assert.AreEqual(1.0, n.StdDev);
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}
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/// <summary>
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/// Can create normal.
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/// </summary>
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/// <param name="mean">Mean value.</param>
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/// <param name="sdev">Standard deviation value.</param>
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[TestCase(0.0, 0.0)]
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[TestCase(10.0, 0.1)]
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[TestCase(-5.0, 1.0)]
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[TestCase(0.0, 10.0)]
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[TestCase(10.0, 100.0)]
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[TestCase(-5.0, Double.PositiveInfinity)]
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public void CanCreateNormal(double mean, double sdev)
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{
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var n = new Normal(mean, sdev);
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Assert.AreEqual(mean, n.Mean);
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Assert.AreEqual(sdev, n.StdDev);
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}
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/// <summary>
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/// Normal create fails with bad parameters.
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/// </summary>
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/// <param name="mean">Mean value.</param>
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/// <param name="sdev">Standard deviation value.</param>
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[TestCase(Double.NaN, 1.0)]
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[TestCase(1.0, Double.NaN)]
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[TestCase(Double.NaN, Double.NaN)]
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[TestCase(1.0, -1.0)]
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public void NormalCreateFailsWithBadParameters(double mean, double sdev)
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{
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Assert.Throws<ArgumentOutOfRangeException>(() => new Normal(mean, sdev));
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}
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/// <summary>
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/// Can create normal from mean and standard deviation.
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/// </summary>
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/// <param name="mean">Mean value.</param>
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/// <param name="sdev">Standard deviation value.</param>
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[TestCase(0.0, 0.0)]
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[TestCase(10.0, 0.1)]
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[TestCase(-5.0, 1.0)]
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[TestCase(0.0, 10.0)]
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[TestCase(10.0, 100.0)]
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[TestCase(-5.0, Double.PositiveInfinity)]
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public void CanCreateNormalFromMeanAndStdDev(double mean, double sdev)
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{
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var n = Normal.WithMeanStdDev(mean, sdev);
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Assert.AreEqual(mean, n.Mean);
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Assert.AreEqual(sdev, n.StdDev);
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}
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/// <summary>
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/// Can create normal from mean and variance.
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/// </summary>
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/// <param name="mean">Mean value.</param>
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/// <param name="var">Variance value.</param>
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[TestCase(0.0, 0.0)]
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[TestCase(10.0, 0.1)]
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[TestCase(-5.0, 1.0)]
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[TestCase(0.0, 10.0)]
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[TestCase(10.0, 100.0)]
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[TestCase(-5.0, Double.PositiveInfinity)]
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public void CanCreateNormalFromMeanAndVariance(double mean, double var)
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{
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var n = Normal.WithMeanVariance(mean, var);
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AssertHelpers.AlmostEqualRelative(mean, n.Mean, 15);
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AssertHelpers.AlmostEqualRelative(var, n.Variance, 15);
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}
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/// <summary>
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/// Can create normal from mean and precision.
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/// </summary>
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/// <param name="mean">Mean value.</param>
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/// <param name="prec">Precision value.</param>
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[TestCase(0.0, 0.0)]
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[TestCase(10.0, 0.1)]
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[TestCase(-5.0, 1.0)]
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[TestCase(0.0, 10.0)]
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[TestCase(10.0, 100.0)]
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[TestCase(-5.0, Double.PositiveInfinity)]
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public void CanCreateNormalFromMeanAndPrecision(double mean, double prec)
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{
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var n = Normal.WithMeanPrecision(mean, prec);
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AssertHelpers.AlmostEqualRelative(mean, n.Mean, 15);
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AssertHelpers.AlmostEqualRelative(prec, n.Precision, 15);
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}
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/// <summary>
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/// Validate ToString.
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/// </summary>
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[Test]
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public void ValidateToString()
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{
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var n = new Normal(1d, 2d);
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Assert.AreEqual("Normal(μ = 1, σ = 2)", n.ToString());
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}
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/// <summary>
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/// Can set precision.
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/// </summary>
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/// <param name="prec">Precision value.</param>
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[TestCase(-0.0)]
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[TestCase(0.0)]
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[TestCase(0.1)]
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[TestCase(1.0)]
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[TestCase(10.0)]
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[TestCase(Double.PositiveInfinity)]
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public void CanSetPrecision(double prec)
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{
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new Normal
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{
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Precision = prec
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};
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}
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/// <summary>
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/// Set precision fails with negative value.
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/// </summary>
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[Test]
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public void SetPrecisionFailsWithNegativePrecision()
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{
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var n = new Normal();
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Assert.Throws<ArgumentOutOfRangeException>(() => n.Precision = -1.0);
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}
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/// <summary>
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/// Can set variance.
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/// </summary>
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/// <param name="var">Variance value.</param>
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[TestCase(-0.0)]
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[TestCase(0.0)]
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[TestCase(0.1)]
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[TestCase(1.0)]
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[TestCase(10.0)]
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[TestCase(Double.PositiveInfinity)]
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public void CanSetVariance(double var)
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{
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var dist = new Normal
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{
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Variance = var
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};
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Assert.AreEqual(var, dist.Variance, 1e-14);
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}
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/// <summary>
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/// Set variance fails with negative value.
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/// </summary>
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[Test]
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public void SetVarianceFailsWithNegativeVariance()
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{
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var n = new Normal();
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Assert.Throws<ArgumentOutOfRangeException>(() => n.Variance = -1.0);
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}
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/// <summary>
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/// Can set standard deviation.
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/// </summary>
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/// <param name="sdev">Standard deviation value.</param>
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[TestCase(-0.0)]
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[TestCase(0.0)]
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[TestCase(0.1)]
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[TestCase(1.0)]
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[TestCase(10.0)]
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[TestCase(Double.PositiveInfinity)]
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public void CanSetStdDev(double sdev)
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{
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var dist = new Normal
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{
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StdDev = sdev
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};
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Assert.AreEqual(sdev, dist.StdDev, 1e-14);
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}
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/// <summary>
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/// Set standard deviation fails with negative value.
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/// </summary>
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[Test]
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public void SetStdDevFailsWithNegativeStdDev()
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{
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var n = new Normal();
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Assert.Throws<ArgumentOutOfRangeException>(() => n.StdDev = -1.0);
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}
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/// <summary>
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/// Can set mean.
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/// </summary>
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/// <param name="mean">Mean value.</param>
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[TestCase(Double.NegativeInfinity)]
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[TestCase(-0.0)]
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[TestCase(0.0)]
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[TestCase(0.1)]
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[TestCase(1.0)]
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[TestCase(10.0)]
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[TestCase(Double.PositiveInfinity)]
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public void CanSetMean(double mean)
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{
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new Normal
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{
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Mean = mean
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};
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}
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/// <summary>
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/// Validate entropy.
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/// </summary>
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/// <param name="sdev">Standard deviation value.</param>
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[TestCase(-0.0)]
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[TestCase(0.0)]
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[TestCase(0.1)]
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[TestCase(1.0)]
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[TestCase(10.0)]
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[TestCase(Double.PositiveInfinity)]
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public void ValidateEntropy(double sdev)
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{
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var n = new Normal(1.0, sdev);
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Assert.AreEqual(Constants.LogSqrt2PiE + Math.Log(n.StdDev), n.Entropy);
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}
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/// <summary>
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/// Validate skewness.
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/// </summary>
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/// <param name="sdev">Standard deviation value.</param>
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[TestCase(-0.0)]
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[TestCase(0.0)]
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[TestCase(0.1)]
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[TestCase(1.0)]
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[TestCase(10.0)]
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[TestCase(Double.PositiveInfinity)]
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public void ValidateSkewness(double sdev)
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{
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var n = new Normal(1.0, sdev);
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Assert.AreEqual(0.0, n.Skewness);
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}
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/// <summary>
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/// Validate mean.
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/// </summary>
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/// <param name="mean">Mean value.</param>
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[TestCase(Double.NegativeInfinity)]
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[TestCase(-0.0)]
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[TestCase(0.0)]
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[TestCase(0.1)]
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[TestCase(1.0)]
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[TestCase(10.0)]
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[TestCase(Double.PositiveInfinity)]
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public void ValidateMode(double mean)
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{
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var n = new Normal(mean, 1.0);
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Assert.AreEqual(mean, n.Mode);
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}
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/// <summary>
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/// Validate median.
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/// </summary>
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/// <param name="mean">Mean value.</param>
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[TestCase(Double.NegativeInfinity)]
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[TestCase(-0.0)]
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[TestCase(0.0)]
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[TestCase(0.1)]
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[TestCase(1.0)]
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[TestCase(10.0)]
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[TestCase(Double.PositiveInfinity)]
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public void ValidateMedian(double mean)
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{
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var n = new Normal(mean, 1.0);
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Assert.AreEqual(mean, n.Median);
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}
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/// <summary>
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/// Validate minimum.
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/// </summary>
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[Test]
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public void ValidateMinimum()
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{
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var n = new Normal();
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Assert.AreEqual(Double.NegativeInfinity, n.Minimum);
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}
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/// <summary>
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/// Validate maximum.
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/// </summary>
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[Test]
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public void ValidateMaximum()
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{
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var n = new Normal();
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Assert.AreEqual(Double.PositiveInfinity, n.Maximum);
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}
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/// <summary>
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/// Validate density.
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/// </summary>
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/// <param name="mean">Mean value.</param>
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/// <param name="sdev">Standard deviation value.</param>
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[TestCase(0.0, 0.0)]
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[TestCase(10.0, 0.1)]
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[TestCase(-5.0, 1.0)]
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[TestCase(0.0, 10.0)]
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[TestCase(10.0, 100.0)]
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[TestCase(-5.0, Double.PositiveInfinity)]
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public void ValidateDensity(double mean, double sdev)
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{
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var n = Normal.WithMeanStdDev(mean, sdev);
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for (var i = 0; i < 11; i++)
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{
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var x = i - 5.0;
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var d = (mean - x) / sdev;
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var pdf = Math.Exp(-0.5 * d * d) / (sdev * Constants.Sqrt2Pi);
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Assert.AreEqual(pdf, n.Density(x));
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Assert.AreEqual(pdf, Normal.PDF(mean, sdev, x));
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}
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}
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/// <summary>
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/// Validate density log.
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/// </summary>
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/// <param name="mean">Mean value.</param>
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/// <param name="sdev">Standard deviation value.</param>
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[TestCase(0.0, 0.0)]
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[TestCase(10.0, 0.1)]
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[TestCase(-5.0, 1.0)]
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[TestCase(0.0, 10.0)]
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[TestCase(10.0, 100.0)]
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[TestCase(-5.0, Double.PositiveInfinity)]
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public void ValidateDensityLn(double mean, double sdev)
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{
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var n = Normal.WithMeanStdDev(mean, sdev);
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for (var i = 0; i < 11; i++)
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{
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var x = i - 5.0;
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var d = (mean - x) / sdev;
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var pdfln = (-0.5 * (d * d)) - Math.Log(sdev) - Constants.LogSqrt2Pi;
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Assert.AreEqual(pdfln, n.DensityLn(x));
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Assert.AreEqual(pdfln, Normal.PDFLn(mean, sdev, x));
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}
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}
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/// <summary>
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/// Can sample static.
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/// </summary>
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[Test]
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public void CanSampleStatic()
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{
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Normal.Sample(new Random(), 0.0, 1.0);
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}
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/// <summary>
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/// Can sample sequence static.
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/// </summary>
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[Test]
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public void CanSampleSequenceStatic()
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{
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var ied = Normal.Samples(new Random(), 0.0, 1.0);
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ied.Take(5).ToArray();
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}
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/// <summary>
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/// Fail sample static with bad parameters.
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/// </summary>
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[Test]
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public void FailSampleStatic()
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{
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Assert.Throws<ArgumentOutOfRangeException>(() => { var d = Normal.Sample(new Random(), 0.0, -1.0); });
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}
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/// <summary>
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/// Fail sample sequence static with bad parameters.
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/// </summary>
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[Test]
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public void FailSampleSequenceStatic()
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{
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Assert.Throws<ArgumentOutOfRangeException>(() => { var ied = Normal.Samples(new Random(), 0.0, -1.0).First(); });
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}
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/// <summary>
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/// Can sample.
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/// </summary>
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[Test]
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public void CanSample()
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{
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var n = new Normal();
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n.Sample();
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}
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/// <summary>
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/// Can sample sequence.
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/// </summary>
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[Test]
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public void CanSampleSequence()
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{
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var n = new Normal();
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var ied = n.Samples();
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ied.Take(5).ToArray();
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}
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/// <summary>
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/// Validate cumulative distribution.
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/// </summary>
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/// <param name="x">Input X value.</param>
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/// <param name="f">Expected value.</param>
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[TestCase(Double.NegativeInfinity, 0.0)]
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[TestCase(-5.0, 0.00000028665157187919391167375233287464535385442301361187883)]
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[TestCase(-2.0, 0.0002326290790355250363499258867279847735487493358890356)]
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[TestCase(-0.0, 0.0062096653257761351669781045741922211278977469230927036)]
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[TestCase(0.0, 0.0062096653257761351669781045741922211278977469230927036)]
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[TestCase(4.0, 0.30853753872598689636229538939166226011639782444542207)]
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[TestCase(5.0, 0.5)]
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[TestCase(6.0, 0.69146246127401310363770461060833773988360217555457859)]
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[TestCase(10.0, 0.9937903346742238648330218954258077788721022530769078)]
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[TestCase(Double.PositiveInfinity, 1.0)]
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public void ValidateCumulativeDistribution(double x, double f)
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{
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var n = Normal.WithMeanStdDev(5.0, 2.0);
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AssertHelpers.AlmostEqualRelative(f, n.CumulativeDistribution(x), 9);
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AssertHelpers.AlmostEqualRelative(f, Normal.CDF(5.0, 2.0, x), 9);
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}
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/// <summary>
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/// Validate inverse cumulative distribution.
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/// </summary>
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/// <param name="x">Input X value.</param>
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/// <param name="f">Expected value.</param>
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[TestCase(Double.NegativeInfinity, 0.0)]
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[TestCase(-5.0, 0.00000028665157187919391167375233287464535385442301361187883)]
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[TestCase(-2.0, 0.0002326290790355250363499258867279847735487493358890356)]
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[TestCase(-0.0, 0.0062096653257761351669781045741922211278977469230927036)]
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[TestCase(0.0, .0062096653257761351669781045741922211278977469230927036)]
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[TestCase(4.0, .30853753872598689636229538939166226011639782444542207)]
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[TestCase(5.0, .5)]
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[TestCase(6.0, .69146246127401310363770461060833773988360217555457859)]
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[TestCase(10.0, 0.9937903346742238648330218954258077788721022530769078)]
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[TestCase(Double.PositiveInfinity, 1.0)]
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public void ValidateInverseCumulativeDistribution(double x, double f)
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{
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var n = Normal.WithMeanStdDev(5.0, 2.0);
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AssertHelpers.AlmostEqualRelative(x, n.InverseCumulativeDistribution(f), 14);
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AssertHelpers.AlmostEqualRelative(x, Normal.InvCDF(5.0, 2.0, f), 14);
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}
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/// <summary>
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/// Can estimate distribution parameters.
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/// </summary>
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[TestCase(0.0, 0.0)]
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[TestCase(10.0, 0.1)]
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[TestCase(-5.0, 1.0)]
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[TestCase(0.0, 5.0)]
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[TestCase(10.0, 50.0)]
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public void CanEstimateParameters(double mean, double stddev)
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{
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var original = new Normal(mean, stddev, new Random(100));
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var estimated = Normal.Estimate(original.Samples().Take(10000));
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AssertHelpers.AlmostEqualRelative(mean, estimated.Mean, 1);
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AssertHelpers.AlmostEqualRelative(stddev, estimated.StdDev, 1);
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}
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}
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}
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|