Distributions: Gamma.InvCDF

src/Numerics/Distributions/Gamma.cs

@@ -360,6 +360,18 @@ namespace MathNet.Numerics.Distributions
             return CDF(_shape, _rate, x);
         }
 
+        /// <summary>
+        /// Computes the inverse of the cumulative distribution function (InvCDF) for the distribution
+        /// at the given probability. This is also known as the quantile or percent point function.
+        /// </summary>
+        /// <param name="p">The location at which to compute the inverse cumulative density.</param>
+        /// <returns>the inverse cumulative density at <paramref name="p"/>.</returns>
+        /// <seealso cref="InvCDF"/>
+        public double InverseCumulativeDistribution(double p)
+        {
+            return InvCDF(_shape, _rate, p);
+        }
+
         /// <summary>
         /// Generates a sample from the Gamma distribution.
         /// </summary>
@@ -491,6 +503,22 @@ namespace MathNet.Numerics.Distributions
             return SpecialFunctions.GammaLowerRegularized(shape, x*rate);
         }
 
+        /// <summary>
+        /// Computes the inverse of the cumulative distribution function (InvCDF) for the distribution
+        /// at the given probability. This is also known as the quantile or percent point function.
+        /// </summary>
+        /// <param name="p">The location at which to compute the inverse cumulative density.</param>
+        /// <param name="shape">The shape (k, α) of the Gamma distribution. Range: α ≥ 0.</param>
+        /// <param name="rate">The rate or inverse scale (β) of the Gamma distribution. Range: β ≥ 0.</param>
+        /// <returns>the inverse cumulative density at <paramref name="p"/>.</returns>
+        /// <seealso cref="InverseCumulativeDistribution"/>
+        public static double InvCDF(double shape, double rate, double p)
+        {
+            if (shape < 0.0 || rate < 0.0) throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
+
+            return SpecialFunctions.GammaLowerRegularizedInv(shape, p)/rate;
+        }
+
         /// <summary>
         /// Generates a sample from the Gamma distribution.
         /// </summary>

src/UnitTests/DistributionTests/Continuous/GammaTests.cs

@@ -498,9 +498,30 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         [TestCase(10, Double.PositiveInfinity, 10.0, 1.0)]
         public void ValidateCumulativeDistribution(int shape, double invScale, double x, double cdf)
         {
-            var n = new Gamma(shape, invScale);
-            AssertHelpers.AlmostEqualRelative(cdf, n.CumulativeDistribution(x), 13);
-            AssertHelpers.AlmostEqualRelative(cdf, Gamma.CDF(shape, invScale, x), 13);
+            var gamma = new Gamma(shape, invScale);
+            Assert.That(gamma.CumulativeDistribution(x), Is.EqualTo(cdf).Within(13));
+            Assert.That(Gamma.CDF(shape, invScale, x), Is.EqualTo(cdf).Within(13));
+        }
+
+        /// <summary>
+        /// Validate inverse cumulative distribution.
+        /// </summary>
+        /// <param name="shape">Shape value.</param>
+        /// <param name="invScale">Inverse scale value.</param>
+        /// <param name="x">Input X value.</param>
+        /// <param name="cdf">Expected value.</param>
+        [TestCase(1, 0.1, 1.0, 0.095162581964040431858607615783064404690935346242622848)]
+        [TestCase(1, 0.1, 10.0, 0.63212055882855767840447622983853913255418886896823196)]
+        [TestCase(1, 1.0, 1.0, 0.63212055882855767840447622983853913255418886896823196)]
+        [TestCase(1, 1.0, 10.0, 0.99995460007023751514846440848443944938976208191113396)]
+        [TestCase(10, 10.0, 1.0, 0.54207028552814779168583514294066541824736464003242184)]
+        [TestCase(10, 1.0, 1.0, 0.00000011142547833872067735305068724025236288094949815466035)]
+        [TestCase(10, 1.0, 10.0, 0.54207028552814779168583514294066541824736464003242184)]
+        public void ValidateInverseCumulativeDistribution(int shape, double invScale, double x, double cdf)
+        {
+            var gamma = new Gamma(shape, invScale);
+            Assert.That(gamma.InverseCumulativeDistribution(cdf), Is.EqualTo(x).Within(10));
+            Assert.That(Gamma.InvCDF(shape, invScale, cdf), Is.EqualTo(x).Within(10));
         }
     }
 }