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@ -78,7 +78,7 @@ namespace MathNet.Numerics.Distributions |
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/// be initialized with the default <seealso cref="System.Random"/> random number generator.
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/// be initialized with the default <seealso cref="System.Random"/> random number generator.
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/// </summary>
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/// </summary>
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/// <param name="mean">The mean (μ) of the normal distribution.</param>
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/// <param name="mean">The mean (μ) of the normal distribution.</param>
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/// <param name="stddev">The standard deviation (σ) of the normal distribution.</param>
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/// <param name="stddev">The standard deviation (σ) of the normal distribution. Range: σ ≥ 0.</param>
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public Normal(double mean, double stddev) |
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public Normal(double mean, double stddev) |
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{ |
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{ |
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_random = new System.Random(); |
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_random = new System.Random(); |
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@ -90,7 +90,7 @@ namespace MathNet.Numerics.Distributions |
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/// be initialized with the default <seealso cref="System.Random"/> random number generator.
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/// be initialized with the default <seealso cref="System.Random"/> random number generator.
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/// </summary>
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/// </summary>
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/// <param name="mean">The mean (μ) of the normal distribution.</param>
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/// <param name="mean">The mean (μ) of the normal distribution.</param>
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/// <param name="stddev">The standard deviation (σ) of the normal distribution.</param>
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/// <param name="stddev">The standard deviation (σ) of the normal distribution. Range: σ ≥ 0.</param>
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/// <param name="randomSource">The random number generator which is used to draw random samples.</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 Normal(double mean, double stddev, System.Random randomSource) |
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public Normal(double mean, double stddev, System.Random randomSource) |
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{ |
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{ |
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@ -99,48 +99,51 @@ namespace MathNet.Numerics.Distributions |
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} |
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} |
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/// <summary>
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/// <summary>
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/// Constructs a normal distribution from a mean and standard deviation. The distribution will
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/// Constructs a normal distribution from a mean and standard deviation.
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/// be initialized with the default <seealso cref="System.Random"/> random number generator.
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/// </summary>
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/// </summary>
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/// <param name="mean">The mean (μ) of the normal distribution.</param>
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/// <param name="mean">The mean (μ) of the normal distribution.</param>
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/// <param name="stddev">The standard deviation (σ) of the normal distribution.</param>
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/// <param name="stddev">The standard deviation (σ) of the normal distribution. Range: σ ≥ 0.</param>
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/// <param name="randomSource">The random number generator which is used to draw random samples. Optional, can be null.</param>
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/// <returns>a normal distribution.</returns>
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/// <returns>a normal distribution.</returns>
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public static Normal WithMeanStdDev(double mean, double stddev) |
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public static Normal WithMeanStdDev(double mean, double stddev, System.Random randomSource = null) |
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{ |
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{ |
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return new Normal(mean, stddev); |
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return new Normal(mean, stddev, randomSource); |
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} |
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} |
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/// <summary>
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/// <summary>
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/// Constructs a normal distribution from a mean and variance. The distribution will
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/// Constructs a normal distribution from a mean and variance.
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/// be initialized with the default <seealso cref="System.Random"/> random number generator.
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/// </summary>
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/// </summary>
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/// <param name="mean">The mean (μ) of the normal distribution.</param>
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/// <param name="mean">The mean (μ) of the normal distribution.</param>
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/// <param name="var">The variance of the normal distribution.</param>
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/// <param name="var">The variance (σ^2) of the normal distribution.</param>
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/// <returns>a normal distribution.</returns>
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/// <param name="randomSource">The random number generator which is used to draw random samples. Optional, can be null.</param>
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public static Normal WithMeanVariance(double mean, double var) |
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/// <returns>A normal distribution.</returns>
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public static Normal WithMeanVariance(double mean, double var, System.Random randomSource = null) |
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{ |
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{ |
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return new Normal(mean, Math.Sqrt(var)); |
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return new Normal(mean, Math.Sqrt(var), randomSource); |
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} |
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} |
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/// <summary>
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/// <summary>
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/// Constructs a normal distribution from a mean and precision. The distribution will
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/// Constructs a normal distribution from a mean and precision.
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/// be initialized with the default <seealso cref="System.Random"/> random number generator.
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/// </summary>
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/// </summary>
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/// <param name="mean">The mean (μ) of the normal distribution.</param>
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/// <param name="mean">The mean (μ) of the normal distribution.</param>
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/// <param name="precision">The precision of the normal distribution.</param>
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/// <param name="precision">The precision of the normal distribution.</param>
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/// <returns>a normal distribution.</returns>
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/// <param name="randomSource">The random number generator which is used to draw random samples. Optional, can be null.</param>
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public static Normal WithMeanPrecision(double mean, double precision) |
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/// <returns>A normal distribution.</returns>
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public static Normal WithMeanPrecision(double mean, double precision, System.Random randomSource = null) |
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{ |
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{ |
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return new Normal(mean, 1.0/Math.Sqrt(precision)); |
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return new Normal(mean, 1.0/Math.Sqrt(precision), randomSource); |
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} |
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} |
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/// <summary>
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/// <summary>
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/// Estimates the normal distribution parameters from sample data with maximum-likelihood.
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/// Estimates the normal distribution parameters from sample data with maximum-likelihood.
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/// </summary>
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/// </summary>
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public static Normal Estimate(IEnumerable<double> samples) |
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/// <param name="samples">The samples to estimate the distribution parameters from.</param>
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/// <param name="randomSource">The random number generator which is used to draw random samples. Optional, can be null.</param>
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/// <returns>A normal distribution.</returns>
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public static Normal Estimate(IEnumerable<double> samples, System.Random randomSource = null) |
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{ |
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{ |
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var meanVariance = samples.MeanVariance(); |
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var meanVariance = samples.MeanVariance(); |
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return new Normal(meanVariance.Item1, Math.Sqrt(meanVariance.Item2)); |
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return new Normal(meanVariance.Item1, Math.Sqrt(meanVariance.Item2), randomSource); |
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} |
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} |
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/// <summary>
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/// <summary>
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@ -152,26 +155,15 @@ namespace MathNet.Numerics.Distributions |
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return "Normal(μ = " + _mean + ", σ = " + _stdDev + ")"; |
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return "Normal(μ = " + _mean + ", σ = " + _stdDev + ")"; |
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} |
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} |
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/// <summary>
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/// Checks whether the parameters of the distribution are valid.
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/// </summary>
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/// <param name="mean">The mean (μ) of the normal distribution.</param>
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/// <param name="stddev">The standard deviation (σ) of the normal distribution.</param>
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/// <returns><c>true</c> when the parameters are valid, <c>false</c> otherwise.</returns>
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static bool IsValidParameterSet(double mean, double stddev) |
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{ |
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return stddev >= 0.0 && !Double.IsNaN(mean); |
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} |
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/// <summary>
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/// <summary>
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/// Sets the parameters of the distribution after checking their validity.
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/// Sets the parameters of the distribution after checking their validity.
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/// </summary>
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/// </summary>
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/// <param name="mean">The mean (μ) of the normal distribution.</param>
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/// <param name="mean">The mean (μ) of the normal distribution.</param>
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/// <param name="stddev">The standard deviation (σ) of the normal distribution.</param>
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/// <param name="stddev">The standard deviation (σ) of the normal distribution. Range: σ ≥ 0.</param>
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/// <exception cref="ArgumentOutOfRangeException">When the parameters don't pass the <see cref="IsValidParameterSet"/> function.</exception>
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/// <exception cref="ArgumentOutOfRangeException">When the parameters are out of range.</exception>
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void SetParameters(double mean, double stddev) |
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void SetParameters(double mean, double stddev) |
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{ |
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{ |
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if (Control.CheckDistributionParameters && !IsValidParameterSet(mean, stddev)) |
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if (stddev < 0.0 || Double.IsNaN(mean) || Double.IsNaN(stddev)) |
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{ |
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{ |
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throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters); |
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throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters); |
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} |
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} |
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@ -190,7 +182,7 @@ namespace MathNet.Numerics.Distributions |
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} |
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} |
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/// <summary>
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/// <summary>
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/// Gets or sets the standard deviation (σ) of the normal distribution.
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/// Gets or sets the standard deviation (σ) of the normal distribution. Range: σ ≥ 0.
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/// </summary>
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/// </summary>
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public double StdDev |
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public double StdDev |
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{ |
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{ |
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@ -203,7 +195,7 @@ namespace MathNet.Numerics.Distributions |
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/// </summary>
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/// </summary>
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public double Variance |
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public double Variance |
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{ |
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{ |
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get { return _stdDev * _stdDev; } |
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get { return _stdDev*_stdDev; } |
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set { SetParameters(_mean, Math.Sqrt(value)); } |
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set { SetParameters(_mean, Math.Sqrt(value)); } |
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} |
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} |
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@ -212,10 +204,10 @@ namespace MathNet.Numerics.Distributions |
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/// </summary>
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/// </summary>
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public double Precision |
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public double Precision |
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{ |
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{ |
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get { return 1.0 / (_stdDev * _stdDev); } |
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get { return 1.0/(_stdDev*_stdDev); } |
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set |
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set |
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{ |
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{ |
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var sdev = 1.0 / Math.Sqrt(value); |
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var sdev = 1.0/Math.Sqrt(value); |
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// Handle the case when the precision is -0.
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// Handle the case when the precision is -0.
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if (Double.IsInfinity(sdev)) |
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if (Double.IsInfinity(sdev)) |
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{ |
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{ |
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@ -283,71 +275,35 @@ namespace MathNet.Numerics.Distributions |
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} |
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} |
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/// <summary>
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/// <summary>
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/// Computes the density of the normal distribution (PDF), i.e. dP(X <= x)/dx.
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/// Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
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/// </summary>
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/// <param name="mean">The mean (μ) of the normal distribution.</param>
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/// <param name="stddev">The standard deviation (σ) of the normal distribution.</param>
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/// <param name="x">The location at which to compute the density.</param>
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/// <returns>the density at <paramref name="x"/>.</returns>
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internal static double Density(double mean, double stddev, double x) |
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{ |
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var d = (x - mean)/stddev; |
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return Math.Exp(-0.5*d*d)/(Constants.Sqrt2Pi*stddev); |
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} |
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/// <summary>
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/// Computes the log density of the normal distribution (lnPDF), i.e. ln(dP(X <= x)/dx).
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/// </summary>
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/// <param name="mean">The mean (μ) of the normal distribution.</param>
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/// <param name="stddev">The standard deviation (σ) of the normal distribution.</param>
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/// <param name="x">The location at which to compute the density.</param>
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/// <returns>the log density at <paramref name="x"/>.</returns>
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internal static double DensityLn(double mean, double stddev, double x) |
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{ |
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var d = (x - mean)/stddev; |
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return (-0.5*d*d) - Math.Log(stddev) - Constants.LogSqrt2Pi; |
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} |
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/// <summary>
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/// Computes the probability density of the distribution (PDF) at x, i.e. dP(X <= x)/dx.
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/// </summary>
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/// </summary>
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/// <param name="x">The location at which to compute the density.</param>
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/// <param name="x">The location at which to compute the density.</param>
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/// <returns>the density at <paramref name="x"/>.</returns>
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/// <returns>the density at <paramref name="x"/>.</returns>
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public double Density(double x) |
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public double Density(double x) |
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{ |
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{ |
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return Density(_mean, _stdDev, x); |
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var d = (x - _mean)/_stdDev; |
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return Math.Exp(-0.5*d*d)/(Constants.Sqrt2Pi*_stdDev); |
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} |
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} |
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/// <summary>
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/// <summary>
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/// Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(dP(X <= x)/dx).
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/// Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
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/// </summary>
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/// </summary>
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/// <param name="x">The location at which to compute the log density.</param>
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/// <param name="x">The location at which to compute the log density.</param>
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/// <returns>the log density at <paramref name="x"/>.</returns>
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/// <returns>the log density at <paramref name="x"/>.</returns>
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public double DensityLn(double x) |
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public double DensityLn(double x) |
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{ |
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{ |
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return DensityLn(_mean, _stdDev, x); |
|
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var d = (x - _mean)/_stdDev; |
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return (-0.5*d*d) - Math.Log(_stdDev) - Constants.LogSqrt2Pi; |
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} |
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} |
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/// <summary>
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|
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/// <summary>
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|
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/// Computes the cumulative distribution function (CDF) of the normal distribution, i.e. P(X <= x).
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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="mean">The mean (μ) of the normal distribution.</param>
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/// <param name="stddev">The standard deviation (σ) of the normal distribution.</param>
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/// <param name="x">The location at which to compute the cumulative density.</param>
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/// <returns>the cumulative density at <paramref name="x"/>.</returns>
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|
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internal static double CumulativeDistribution(double mean, double stddev, double x) |
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|
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{ |
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|
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return 0.5*(1.0 + SpecialFunctions.Erf((x - mean)/(stddev*Constants.Sqrt2))); |
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} |
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/// <summary>
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|
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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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|
/// </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="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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|
|
/// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
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|
|
public double CumulativeDistribution(double x) |
|
|
public double CumulativeDistribution(double x) |
|
|
{ |
|
|
{ |
|
|
return CumulativeDistribution(_mean, _stdDev, x); |
|
|
return 0.5*(1.0 + SpecialFunctions.Erf((x - _mean)/(_stdDev*Constants.Sqrt2))); |
|
|
} |
|
|
} |
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|
|
/// <summary>
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|
|
/// <summary>
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|
@ -361,6 +317,29 @@ namespace MathNet.Numerics.Distributions |
|
|
return _mean - (_stdDev*Constants.Sqrt2*SpecialFunctions.ErfcInv(2.0*p)); |
|
|
return _mean - (_stdDev*Constants.Sqrt2*SpecialFunctions.ErfcInv(2.0*p)); |
|
|
} |
|
|
} |
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|
/// <summary>
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|
|
/// Generates a sample from the normal distribution using the <i>Box-Muller</i> algorithm.
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|
/// </summary>
|
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|
|
/// <returns>a sample from the distribution.</returns>
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|
|
public double Sample() |
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|
|
{ |
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|
|
return _mean + (_stdDev*SampleStandardBoxMuller(_random).Item1); |
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|
} |
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|
/// <summary>
|
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|
|
/// Generates a sequence of samples from the normal distribution using the <i>Box-Muller</i> algorithm.
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|
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|
|
/// </summary>
|
|
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|
|
/// <returns>a sequence of samples from the distribution.</returns>
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|
|
public IEnumerable<double> Samples() |
|
|
|
|
|
{ |
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|
|
while (true) |
|
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|
|
{ |
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|
|
var sample = SampleStandardBoxMuller(_random); |
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|
|
yield return _mean + (_stdDev*sample.Item1); |
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|
|
yield return _mean + (_stdDev*sample.Item2); |
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|
} |
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|
} |
|
|
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|
|
/// <summary>
|
|
|
/// <summary>
|
|
|
/// Samples a pair of standard normal distributed random variables using the <i>Box-Muller</i> algorithm.
|
|
|
/// Samples a pair of standard normal distributed random variables using the <i>Box-Muller</i> algorithm.
|
|
|
/// </summary>
|
|
|
/// </summary>
|
|
|
@ -368,65 +347,77 @@ namespace MathNet.Numerics.Distributions |
|
|
/// <returns>a pair of random numbers from the standard normal distribution.</returns>
|
|
|
/// <returns>a pair of random numbers from the standard normal distribution.</returns>
|
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static Tuple<double, double> SampleStandardBoxMuller(System.Random rnd) |
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static Tuple<double, double> SampleStandardBoxMuller(System.Random rnd) |
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{ |
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{ |
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var v1 = (2.0*rnd.NextDouble()) - 1.0; |
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var v1 = (2.0 * rnd.NextDouble()) - 1.0; |
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var v2 = (2.0*rnd.NextDouble()) - 1.0; |
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var v2 = (2.0 * rnd.NextDouble()) - 1.0; |
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var r = (v1*v1) + (v2*v2); |
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var r = (v1 * v1) + (v2 * v2); |
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while (r >= 1.0 || r == 0.0) |
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while (r >= 1.0 || r == 0.0) |
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{ |
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{ |
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v1 = (2.0*rnd.NextDouble()) - 1.0; |
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v1 = (2.0 * rnd.NextDouble()) - 1.0; |
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v2 = (2.0*rnd.NextDouble()) - 1.0; |
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v2 = (2.0 * rnd.NextDouble()) - 1.0; |
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r = (v1*v1) + (v2*v2); |
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r = (v1 * v1) + (v2 * v2); |
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} |
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} |
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var fac = Math.Sqrt(-2.0*Math.Log(r)/r); |
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var fac = Math.Sqrt(-2.0 * Math.Log(r) / r); |
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return new Tuple<double, double>(v1*fac, v2*fac); |
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return new Tuple<double, double>(v1 * fac, v2 * fac); |
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} |
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} |
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/// <summary>
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/// <summary>
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/// Samples the distribution.
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/// Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
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/// </summary>
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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="mean">The mean (μ) of the normal distribution.</param>
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/// <param name="mean">The mean (μ) of the normal distribution.</param>
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/// <param name="stddev">The standard deviation (σ) of the normal distribution.</param>
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/// <param name="stddev">The standard deviation (σ) of the normal distribution. Range: σ ≥ 0.</param>
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/// <returns>a random number from the distribution.</returns>
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/// <param name="x">The location at which to compute the density.</param>
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internal static double SampleUnchecked(System.Random rnd, double mean, double stddev) |
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/// <returns>the density at <paramref name="x"/>.</returns>
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public static double PDF(double mean, double stddev, double x) |
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{ |
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{ |
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return mean + (stddev*SampleStandardBoxMuller(rnd).Item1); |
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if (stddev < 0.0) throw new ArgumentOutOfRangeException("stddev", Resources.InvalidDistributionParameters); |
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var d = (x - mean)/stddev; |
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return Math.Exp(-0.5*d*d)/(Constants.Sqrt2Pi*stddev); |
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} |
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} |
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/// <summary>
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/// <summary>
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/// Samples the distribution.
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/// Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
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/// </summary>
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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="mean">The mean (μ) of the normal distribution.</param>
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/// <param name="mean">The mean (μ) of the normal distribution.</param>
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/// <param name="stddev">The standard deviation (σ) of the normal distribution.</param>
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/// <param name="stddev">The standard deviation (σ) of the normal distribution. Range: σ ≥ 0.</param>
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/// <returns>a random number from the distribution.</returns>
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/// <param name="x">The location at which to compute the density.</param>
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internal static IEnumerable<double> SamplesUnchecked(System.Random rnd, double mean, double stddev) |
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/// <returns>the log density at <paramref name="x"/>.</returns>
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public static double PDFLn(double mean, double stddev, double x) |
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{ |
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{ |
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while (true) |
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if (stddev < 0.0) throw new ArgumentOutOfRangeException("stddev", Resources.InvalidDistributionParameters); |
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{ |
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var sample = SampleStandardBoxMuller(rnd); |
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var d = (x - mean)/stddev; |
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yield return mean + (stddev*sample.Item1); |
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return (-0.5*d*d) - Math.Log(stddev) - Constants.LogSqrt2Pi; |
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yield return mean + (stddev*sample.Item2); |
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} |
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} |
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} |
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/// <summary>
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/// <summary>
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/// Generates a sample from the normal distribution using the <i>Box-Muller</i> algorithm.
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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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/// </summary>
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/// <returns>a sample from the distribution.</returns>
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/// <param name="x">The location at which to compute the cumulative distribution function.</param>
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public double Sample() |
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/// <param name="mean">The mean (μ) of the normal distribution.</param>
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/// <param name="stddev">The standard deviation (σ) of the normal distribution. Range: σ ≥ 0.</param>
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/// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
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public static double CDF(double mean, double stddev, double x) |
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{ |
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{ |
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return SampleUnchecked(_random, _mean, _stdDev); |
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if (stddev < 0.0) throw new ArgumentOutOfRangeException("stddev", Resources.InvalidDistributionParameters); |
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return 0.5*(1.0 + SpecialFunctions.Erf((x - mean)/(stddev*Constants.Sqrt2))); |
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} |
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} |
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/// <summary>
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/// <summary>
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/// Generates a sequence of samples from the normal distribution using the <i>Box-Muller</i> algorithm.
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/// Computes the inverse of the cumulative distribution function (InvCDF) for the distribution
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/// at the given probability.
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/// </summary>
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/// </summary>
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/// <returns>a sequence of samples from the distribution.</returns>
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/// <param name="p">The location at which to compute the inverse cumulative density.</param>
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public IEnumerable<double> Samples() |
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/// <param name="mean">The mean (μ) of the normal distribution.</param>
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/// <param name="stddev">The standard deviation (σ) of the normal distribution. Range: σ ≥ 0.</param>
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/// <returns>the inverse cumulative density at <paramref name="p"/>.</returns>
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public static double InvCDF(double mean, double stddev, double p) |
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{ |
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{ |
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return SamplesUnchecked(_random, _mean, _stdDev); |
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if (stddev < 0.0) throw new ArgumentOutOfRangeException("stddev", Resources.InvalidDistributionParameters); |
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return mean - (stddev*Constants.Sqrt2*SpecialFunctions.ErfcInv(2.0*p)); |
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} |
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} |
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/// <summary>
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/// <summary>
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@ -434,16 +425,13 @@ namespace MathNet.Numerics.Distributions |
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/// </summary>
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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="rnd">The random number generator to use.</param>
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/// <param name="mean">The mean (μ) of the normal distribution.</param>
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/// <param name="mean">The mean (μ) of the normal distribution.</param>
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/// <param name="stddev">The standard deviation (σ) of the normal distribution.</param>
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/// <param name="stddev">The standard deviation (σ) of the normal distribution. Range: σ ≥ 0.</param>
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/// <returns>a sample from the distribution.</returns>
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/// <returns>a sample from the distribution.</returns>
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public static double Sample(System.Random rnd, double mean, double stddev) |
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public static double Sample(System.Random rnd, double mean, double stddev) |
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{ |
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{ |
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if (Control.CheckDistributionParameters && !IsValidParameterSet(mean, stddev)) |
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if (stddev < 0.0) throw new ArgumentOutOfRangeException("stddev", Resources.InvalidDistributionParameters); |
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{ |
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throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters); |
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} |
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return SampleUnchecked(rnd, mean, stddev); |
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return mean + (stddev*SampleStandardBoxMuller(rnd).Item1); |
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} |
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} |
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/// <summary>
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/// <summary>
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@ -451,16 +439,18 @@ namespace MathNet.Numerics.Distributions |
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/// </summary>
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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="rnd">The random number generator to use.</param>
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/// <param name="mean">The mean (μ) of the normal distribution.</param>
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/// <param name="mean">The mean (μ) of the normal distribution.</param>
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/// <param name="stddev">The standard deviation (σ) of the normal distribution.</param>
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/// <param name="stddev">The standard deviation (σ) of the normal distribution. Range: σ ≥ 0.</param>
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/// <returns>a sequence of samples from the distribution.</returns>
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/// <returns>a sequence of samples from the distribution.</returns>
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public static IEnumerable<double> Samples(System.Random rnd, double mean, double stddev) |
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public static IEnumerable<double> Samples(System.Random rnd, double mean, double stddev) |
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{ |
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{ |
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if (Control.CheckDistributionParameters && !IsValidParameterSet(mean, stddev)) |
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if (stddev < 0.0) throw new ArgumentOutOfRangeException("stddev", Resources.InvalidDistributionParameters); |
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while (true) |
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{ |
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{ |
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throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters); |
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var sample = SampleStandardBoxMuller(rnd); |
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yield return mean + (stddev*sample.Item1); |
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yield return mean + (stddev*sample.Item2); |
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} |
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} |
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return SamplesUnchecked(rnd, mean, stddev); |
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} |
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} |
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} |
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} |
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} |
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} |
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Christoph Ruegg
13 years ago