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Distributions: Migrate PERT from Beta to BetaScaled #321
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‎src/Numerics/Distributions/Beta.cs

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@@ -92,49 +92,6 @@ public Beta(double a, double b, System.Random randomSource)
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_shapeB = b;
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}
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/// <summary>
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/// Create a Beta PERT distribution, used in risk analysis and other domains where an expert forecast
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/// is used to construct an underlying beta distribution.
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/// </summary>
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/// <param name="min">The minimum value.</param>
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/// <param name="max">The maximum value.</param>
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/// <param name="likely">The most likely value (mode).</param>
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/// <param name="randomSource">The random number generator which is used to draw random samples.</param>
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/// <returns>The Beta distribution derived from the PERT parameters.</returns>
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public static Beta PERT(double min, double max, double likely, System.Random randomSource = null)
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{
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if( min > max || likely > max || likely < min )
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{
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throw new ArgumentException(Resources.InvalidDistributionParameters);
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}
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// specified to make the formulas match the literature;
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// traditionally set to 4 so that the range between min and max
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// represents six standard deviations (sometimes called
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// "the six-sigma assumption").
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const double lambda = 4;
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// calculate the mean
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double mean = (min + max + lambda * likely) / (lambda + 2);
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// derive the shape parameters a and b
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double a;
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// special case where mean and mode are identical
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if (mean == likely)
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{
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a = (lambda/2) + 1;
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}
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else
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{
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a = ((mean - min) * (2 * likely - min - max)) / ((likely - mean) * (max - min));
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}
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double b = (a * (max - mean)) / (mean - min);
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return new Beta(a, b, randomSource);
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}
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/// <summary>
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/// A string representation of the distribution.
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/// </summary>

‎src/Numerics/Distributions/BetaScaled.cs

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Original file line numberDiff line numberDiff line change
@@ -88,6 +88,49 @@ public BetaScaled(double a, double b, double location, double scale, System.Rand
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_scale = scale;
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}
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/// <summary>
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/// Create a Beta PERT distribution, used in risk analysis and other domains where an expert forecast
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/// is used to construct an underlying beta distribution.
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/// </summary>
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/// <param name="min">The minimum value.</param>
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/// <param name="max">The maximum value.</param>
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/// <param name="likely">The most likely value (mode).</param>
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/// <param name="randomSource">The random number generator which is used to draw random samples.</param>
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/// <returns>The Beta distribution derived from the PERT parameters.</returns>
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public static BetaScaled PERT(double min, double max, double likely, System.Random randomSource = null)
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{
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if (min > max || likely > max || likely < min)
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{
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throw new ArgumentException(Resources.InvalidDistributionParameters);
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}
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// specified to make the formulas match the literature;
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// traditionally set to 4 so that the range between min and max
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// represents six standard deviations (sometimes called
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// "the six-sigma assumption").
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const double lambda = 4;
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// calculate the mean
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double mean = (min + max + lambda * likely) / (lambda + 2);
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// derive the shape parameters a and b
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double a;
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// special case where mean and mode are identical
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if (mean == likely)
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{
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a = (lambda / 2) + 1;
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}
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else
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{
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a = ((mean - min) * (2 * likely - min - max)) / ((likely - mean) * (max - min));
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}
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double b = (a * (max - mean)) / (mean - min);
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return new BetaScaled(a, b, min, max - min, randomSource);
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}
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/// <summary>
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/// A string representation of the distribution.
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/// </summary>

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