// <copyright file="DiscreteUniform.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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//
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// Copyright (c) 2009-2014 Math.NET
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//
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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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//
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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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//
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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.Collections.Generic;
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using IStation.Numerics.Random;
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namespace IStation.Numerics.Distributions
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{
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/// <summary>
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/// Discrete Univariate Uniform distribution.
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/// The discrete uniform distribution is a distribution over integers. The distribution
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/// is parameterized by a lower and upper bound (both inclusive).
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/// <a href="http://en.wikipedia.org/wiki/Uniform_distribution_%28discrete%29">Wikipedia - Discrete uniform distribution</a>.
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/// </summary>
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public class DiscreteUniform : IDiscreteDistribution
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{
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System.Random _random;
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readonly int _lower;
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readonly int _upper;
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/// <summary>
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/// Initializes a new instance of the DiscreteUniform class.
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/// </summary>
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/// <param name="lower">Lower bound, inclusive. Range: lower ≤ upper.</param>
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/// <param name="upper">Upper bound, inclusive. Range: lower ≤ upper.</param>
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public DiscreteUniform(int lower, int upper)
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{
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if (!IsValidParameterSet(lower, upper))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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_random = SystemRandomSource.Default;
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_lower = lower;
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_upper = upper;
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}
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/// <summary>
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/// Initializes a new instance of the DiscreteUniform class.
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/// </summary>
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/// <param name="lower">Lower bound, inclusive. Range: lower ≤ upper.</param>
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/// <param name="upper">Upper bound, inclusive. Range: lower ≤ upper.</param>
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/// <param name="randomSource">The random number generator which is used to draw random samples.</param>
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public DiscreteUniform(int lower, int upper, System.Random randomSource)
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{
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if (!IsValidParameterSet(lower, upper))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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_random = randomSource ?? SystemRandomSource.Default;
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_lower = lower;
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_upper = upper;
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}
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/// <summary>
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/// Returns a <see cref="System.String"/> that represents this instance.
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/// </summary>
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/// <returns>
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/// A <see cref="System.String"/> that represents this instance.
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/// </returns>
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public override string ToString()
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{
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return $"DiscreteUniform(Lower = {_lower}, Upper = {_upper})";
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}
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/// <summary>
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/// Tests whether the provided values are valid parameters for this distribution.
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/// </summary>
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/// <param name="lower">Lower bound, inclusive. Range: lower ≤ upper.</param>
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/// <param name="upper">Upper bound, inclusive. Range: lower ≤ upper.</param>
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public static bool IsValidParameterSet(int lower, int upper)
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{
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return lower <= upper;
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}
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/// <summary>
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/// Gets the inclusive lower bound of the probability distribution.
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/// </summary>
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public int LowerBound => _lower;
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/// <summary>
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/// Gets the inclusive upper bound of the probability distribution.
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/// </summary>
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public int UpperBound => _upper;
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/// <summary>
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/// Gets or sets the random number generator which is used to draw random samples.
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/// </summary>
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public System.Random RandomSource
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{
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get => _random;
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set => _random = value ?? SystemRandomSource.Default;
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}
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/// <summary>
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/// Gets the mean of the distribution.
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/// </summary>
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public double Mean => (_lower + _upper)/2.0;
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/// <summary>
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/// Gets the standard deviation of the distribution.
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/// </summary>
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public double StdDev => Math.Sqrt((((_upper - _lower + 1.0)*(_upper - _lower + 1.0)) - 1.0)/12.0);
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/// <summary>
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/// Gets the variance of the distribution.
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/// </summary>
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public double Variance => (((_upper - _lower + 1.0)*(_upper - _lower + 1.0)) - 1.0)/12.0;
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/// <summary>
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/// Gets the entropy of the distribution.
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/// </summary>
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public double Entropy => Math.Log(_upper - _lower + 1.0);
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/// <summary>
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/// Gets the skewness of the distribution.
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/// </summary>
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public double Skewness => 0.0;
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/// <summary>
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/// Gets the smallest element in the domain of the distributions which can be represented by an integer.
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/// </summary>
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public int Minimum => _lower;
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/// <summary>
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/// Gets the largest element in the domain of the distributions which can be represented by an integer.
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/// </summary>
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public int Maximum => _upper;
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/// <summary>
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/// Gets the mode of the distribution; since every element in the domain has the same probability this method returns the middle one.
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/// </summary>
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public int Mode => (int)Math.Floor((_lower + _upper)/2.0);
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/// <summary>
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/// Gets the median of the distribution.
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/// </summary>
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public double Median => (_lower + _upper)/2.0;
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/// <summary>
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/// Computes the probability mass (PMF) at k, i.e. P(X = k).
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/// </summary>
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/// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param>
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/// <returns>the probability mass at location <paramref name="k"/>.</returns>
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public double Probability(int k)
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{
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return PMF(_lower, _upper, k);
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}
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/// <summary>
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/// Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
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/// </summary>
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/// <param name="k">The location in the domain where we want to evaluate the log probability mass function.</param>
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/// <returns>the log probability mass at location <paramref name="k"/>.</returns>
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public double ProbabilityLn(int k)
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{
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return PMFLn(_lower, _upper, k);
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}
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/// <summary>
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/// Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
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/// </summary>
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/// <param name="x">The location at which to compute the cumulative distribution function.</param>
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/// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
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public double CumulativeDistribution(double x)
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{
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return CDF(_lower, _upper, x);
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}
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/// <summary>
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/// Computes the probability mass (PMF) at k, i.e. P(X = k).
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/// </summary>
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/// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param>
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/// <param name="lower">Lower bound, inclusive. Range: lower ≤ upper.</param>
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/// <param name="upper">Upper bound, inclusive. Range: lower ≤ upper.</param>
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/// <returns>the probability mass at location <paramref name="k"/>.</returns>
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public static double PMF(int lower, int upper, int k)
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{
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if (!(lower <= upper))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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return k >= lower && k <= upper ? 1.0/(upper - lower + 1) : 0.0;
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}
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/// <summary>
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/// Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
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/// </summary>
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/// <param name="k">The location in the domain where we want to evaluate the log probability mass function.</param>
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/// <param name="lower">Lower bound, inclusive. Range: lower ≤ upper.</param>
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/// <param name="upper">Upper bound, inclusive. Range: lower ≤ upper.</param>
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/// <returns>the log probability mass at location <paramref name="k"/>.</returns>
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public static double PMFLn(int lower, int upper, int k)
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{
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if (!(lower <= upper))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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return k >= lower && k <= upper ? -Math.Log(upper - lower + 1) : double.NegativeInfinity;
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}
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/// <summary>
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/// Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
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/// </summary>
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/// <param name="x">The location at which to compute the cumulative distribution function.</param>
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/// <param name="lower">Lower bound, inclusive. Range: lower ≤ upper.</param>
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/// <param name="upper">Upper bound, inclusive. Range: lower ≤ upper.</param>
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/// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
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/// <seealso cref="CumulativeDistribution"/>
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public static double CDF(int lower, int upper, double x)
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{
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if (!(lower <= upper))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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if (x < lower)
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{
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return 0.0;
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}
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if (x >= upper)
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{
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return 1.0;
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}
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return Math.Min(1.0, (Math.Floor(x) - lower + 1)/(upper - lower + 1));
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}
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/// <summary>
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/// Generates one sample from the discrete uniform distribution. This method does not do any parameter checking.
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/// </summary>
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/// <param name="rnd">The random source to use.</param>
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/// <param name="lower">Lower bound, inclusive. Range: lower ≤ upper.</param>
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/// <param name="upper">Upper bound, inclusive. Range: lower ≤ upper.</param>
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/// <returns>A random sample from the discrete uniform distribution.</returns>
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static int SampleUnchecked(System.Random rnd, int lower, int upper)
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{
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return rnd.Next(lower, upper + 1);
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}
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static void SamplesUnchecked(System.Random rnd, int[] values, int lower, int upper)
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{
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rnd.NextInt32s(values, lower, upper + 1);
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}
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static IEnumerable<int> SamplesUnchecked(System.Random rnd, int lower, int upper)
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{
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return rnd.NextInt32Sequence(lower, upper + 1);
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}
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/// <summary>
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/// Draws a random sample from the distribution.
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/// </summary>
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/// <returns>a sample from the distribution.</returns>
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public int Sample()
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{
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return SampleUnchecked(_random, _lower, _upper);
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}
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/// <summary>
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/// Fills an array with samples generated from the distribution.
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/// </summary>
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public void Samples(int[] values)
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{
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SamplesUnchecked(_random, values, _lower, _upper);
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}
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/// <summary>
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/// Samples an array of uniformly distributed random variables.
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/// </summary>
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/// <returns>a sequence of samples from the distribution.</returns>
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public IEnumerable<int> Samples()
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{
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return SamplesUnchecked(_random, _lower, _upper);
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}
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/// <summary>
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/// Samples a uniformly distributed random variable.
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/// </summary>
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/// <param name="rnd">The random number generator to use.</param>
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/// <param name="lower">Lower bound, inclusive. Range: lower ≤ upper.</param>
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/// <param name="upper">Upper bound, inclusive. Range: lower ≤ upper.</param>
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/// <returns>A sample from the discrete uniform distribution.</returns>
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public static int Sample(System.Random rnd, int lower, int upper)
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{
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if (!(lower <= upper))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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return SampleUnchecked(rnd, lower, upper);
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}
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/// <summary>
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/// Samples a sequence of uniformly distributed random variables.
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/// </summary>
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/// <param name="rnd">The random number generator to use.</param>
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/// <param name="lower">Lower bound, inclusive. Range: lower ≤ upper.</param>
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/// <param name="upper">Upper bound, inclusive. Range: lower ≤ upper.</param>
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/// <returns>a sequence of samples from the discrete uniform distribution.</returns>
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public static IEnumerable<int> Samples(System.Random rnd, int lower, int upper)
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{
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if (!(lower <= upper))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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return SamplesUnchecked(rnd, lower, upper);
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}
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/// <summary>
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/// Fills an array with samples generated from the distribution.
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/// </summary>
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/// <param name="rnd">The random number generator to use.</param>
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/// <param name="values">The array to fill with the samples.</param>
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/// <param name="lower">Lower bound, inclusive. Range: lower ≤ upper.</param>
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/// <param name="upper">Upper bound, inclusive. Range: lower ≤ upper.</param>
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/// <returns>a sequence of samples from the discrete uniform distribution.</returns>
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public static void Samples(System.Random rnd, int[] values, int lower, int upper)
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{
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if (!(lower <= upper))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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SamplesUnchecked(rnd, values, lower, upper);
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}
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/// <summary>
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/// Samples a uniformly distributed random variable.
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/// </summary>
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/// <param name="lower">Lower bound, inclusive. Range: lower ≤ upper.</param>
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/// <param name="upper">Upper bound, inclusive. Range: lower ≤ upper.</param>
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/// <returns>A sample from the discrete uniform distribution.</returns>
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public static int Sample(int lower, int upper)
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{
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if (!(lower <= upper))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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return SampleUnchecked(SystemRandomSource.Default, lower, upper);
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}
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/// <summary>
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/// Samples a sequence of uniformly distributed random variables.
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/// </summary>
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/// <param name="lower">Lower bound, inclusive. Range: lower ≤ upper.</param>
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/// <param name="upper">Upper bound, inclusive. Range: lower ≤ upper.</param>
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/// <returns>a sequence of samples from the discrete uniform distribution.</returns>
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public static IEnumerable<int> Samples(int lower, int upper)
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{
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if (!(lower <= upper))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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return SamplesUnchecked(SystemRandomSource.Default, lower, upper);
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}
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/// <summary>
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/// Fills an array with samples generated from the distribution.
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/// </summary>
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/// <param name="values">The array to fill with the samples.</param>
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/// <param name="lower">Lower bound, inclusive. Range: lower ≤ upper.</param>
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/// <param name="upper">Upper bound, inclusive. Range: lower ≤ upper.</param>
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/// <returns>a sequence of samples from the discrete uniform distribution.</returns>
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public static void Samples(int[] values, int lower, int upper)
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{
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if (!(lower <= upper))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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SamplesUnchecked(SystemRandomSource.Default, values, lower, upper);
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}
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}
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}
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