diff --git a/src/Numerics/Distributions/Exponential.cs b/src/Numerics/Distributions/Exponential.cs
index 5280144d..d06740e2 100644
--- a/src/Numerics/Distributions/Exponential.cs
+++ b/src/Numerics/Distributions/Exponential.cs
@@ -80,16 +80,6 @@ namespace MathNet.Numerics.Distributions
             return "Exponential(λ = " + _rate + ")";
         }
 
-        /// <summary>
-        /// Checks whether the parameters of the distribution are valid. 
-        /// </summary>
-        /// <param name="rate">The rate (λ) parameter of the distribution. Range: λ ≥ 0.</param>
-        /// <returns><c>true</c> when the parameters are valid, <c>false</c> otherwise.</returns>
-        static bool IsValidParameterSet(double rate)
-        {
-            return rate >= 0.0;
-        }
-
         /// <summary>
         /// Sets the parameters of the distribution after checking their validity.
         /// </summary>
@@ -97,7 +87,7 @@ namespace MathNet.Numerics.Distributions
         /// <exception cref="ArgumentOutOfRangeException">When the parameters are out of range.</exception>
         void SetParameters(double rate)
         {
-            if (Control.CheckDistributionParameters && !IsValidParameterSet(rate))
+            if (rate < 0.0 || Double.IsNaN(rate))
             {
                 throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
             }
@@ -200,14 +190,10 @@ namespace MathNet.Numerics.Distributions
         /// </summary>
         /// <param name="x">The location at which to compute the density.</param>
         /// <returns>the density at <paramref name="x"/>.</returns>
+        /// <seealso cref="PDF"/>
         public double Density(double x)
         {
-            if (x >= 0.0)
-            {
-                return _rate*Math.Exp(-_rate*x);
-            }
-
-            return 0.0;
+            return x < 0.0 ? 0.0 : _rate*Math.Exp(-_rate*x);
         }
 
         /// <summary>
@@ -215,6 +201,7 @@ namespace MathNet.Numerics.Distributions
         /// </summary>
         /// <param name="x">The location at which to compute the log density.</param>
         /// <returns>the log density at <paramref name="x"/>.</returns>
+        /// <seealso cref="PDFLn"/>
         public double DensityLn(double x)
         {
             return Math.Log(_rate) - (_rate*x);
@@ -225,14 +212,43 @@ namespace MathNet.Numerics.Distributions
         /// </summary>
         /// <param name="x">The location at which to compute the cumulative distribution function.</param>
         /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
+        /// <seealso cref="CDF"/>
         public double CumulativeDistribution(double x)
         {
-            if (x >= 0.0)
+            return x < 0.0 ? 0.0 : 1.0 - Math.Exp(-_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 p >= 1.0 ? double.PositiveInfinity : -Math.Log(1 - p)/_rate;
+        }
+
+        /// <summary>
+        /// Draws a random sample from the distribution.
+        /// </summary>
+        /// <returns>A random number from this distribution.</returns>
+        public double Sample()
+        {
+            return SampleUnchecked(_random, _rate);
+        }
+
+        /// <summary>
+        /// Generates a sequence of samples from the Exponential distribution.
+        /// </summary>
+        /// <returns>a sequence of samples from the distribution.</returns>
+        public IEnumerable<double> Samples()
+        {
+            while (true)
             {
-                return 1.0 - Math.Exp(-_rate*x);
+                yield return SampleUnchecked(_random, _rate);
             }
-
-            return 0.0;
         }
 
         /// <summary>
@@ -249,28 +265,64 @@ namespace MathNet.Numerics.Distributions
                 r = rnd.NextDouble();
             }
 
-            return -Math.Log(r)/rate;
+            return -Math.Log(r) / rate;
         }
 
         /// <summary>
-        /// Draws a random sample from the distribution.
+        /// Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
         /// </summary>
-        /// <returns>A random number from this distribution.</returns>
-        public double Sample()
+        /// <param name="rate">The rate (λ) parameter of the distribution. Range: λ ≥ 0.</param>
+        /// <param name="x">The location at which to compute the density.</param>
+        /// <returns>the density at <paramref name="x"/>.</returns>
+        /// <seealso cref="Density"/>
+        public static double PDF(double rate, double x)
         {
-            return SampleUnchecked(_random, _rate);
+            if (rate < 0.0) throw new ArgumentOutOfRangeException("rate", Resources.InvalidDistributionParameters);
+
+            return x < 0.0 ? 0.0 : rate*Math.Exp(-rate*x);
         }
 
         /// <summary>
-        /// Generates a sequence of samples from the Exponential distribution.
+        /// Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
         /// </summary>
-        /// <returns>a sequence of samples from the distribution.</returns>
-        public IEnumerable<double> Samples()
+        /// <param name="rate">The rate (λ) parameter of the distribution. Range: λ ≥ 0.</param>
+        /// <param name="x">The location at which to compute the density.</param>
+        /// <returns>the log density at <paramref name="x"/>.</returns>
+        /// <seealso cref="DensityLn"/>
+        public static double PDFLn(double rate, double x)
         {
-            while (true)
-            {
-                yield return SampleUnchecked(_random, _rate);
-            }
+            if (rate < 0.0) throw new ArgumentOutOfRangeException("rate", Resources.InvalidDistributionParameters);
+
+            return Math.Log(rate) - (rate*x);
+        }
+
+        /// <summary>
+        /// Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
+        /// </summary>
+        /// <param name="x">The location at which to compute the cumulative distribution function.</param>
+        /// <param name="rate">The rate (λ) parameter of the distribution. Range: λ ≥ 0.</param>
+        /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
+        /// <seealso cref="CumulativeDistribution"/>
+        public static double CDF(double rate, double x)
+        {
+            if (rate < 0.0) throw new ArgumentOutOfRangeException("rate", Resources.InvalidDistributionParameters);
+
+            return x < 0.0 ? 0.0 : 1.0 - Math.Exp(-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>
+        /// <param name="rate">The rate (λ) parameter of the distribution. Range: λ ≥ 0.</param>
+        /// <returns>the inverse cumulative density at <paramref name="p"/>.</returns>
+        /// <seealso cref="InverseCumulativeDistribution"/>
+        public static double InvCDF(double rate, double p)
+        {
+            if (rate < 0.0) throw new ArgumentOutOfRangeException("rate", Resources.InvalidDistributionParameters);
+
+            return p >= 1.0 ? double.PositiveInfinity : -Math.Log(1 - p)/rate;
         }
 
         /// <summary>
@@ -281,10 +333,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>A random number from this distribution.</returns>
         public static double Sample(System.Random rnd, double rate)
         {
-            if (Control.CheckDistributionParameters && !IsValidParameterSet(rate))
-            {
-                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
-            }
+            if (rate < 0.0) throw new ArgumentOutOfRangeException("rate", Resources.InvalidDistributionParameters);
 
             return SampleUnchecked(rnd, rate);
         }
@@ -297,10 +346,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a sequence of samples from the distribution.</returns>
         public static IEnumerable<double> Samples(System.Random rnd, double rate)
         {
-            if (Control.CheckDistributionParameters && !IsValidParameterSet(rate))
-            {
-                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
-            }
+            if (rate < 0.0) throw new ArgumentOutOfRangeException("rate", Resources.InvalidDistributionParameters);
 
             while (true)
             {
diff --git a/src/UnitTests/DistributionTests/Continuous/ExponentialTests.cs b/src/UnitTests/DistributionTests/Continuous/ExponentialTests.cs
index 5205dcd5..ab55a8a1 100644
--- a/src/UnitTests/DistributionTests/Continuous/ExponentialTests.cs
+++ b/src/UnitTests/DistributionTests/Continuous/ExponentialTests.cs
@@ -266,11 +266,13 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
             var n = new Exponential(lambda);
             if (x >= 0)
             {
-                Assert.AreEqual(lambda * Math.Exp(-lambda * x), n.Density(x));
+                Assert.AreEqual(lambda*Math.Exp(-lambda*x), n.Density(x));
+                Assert.AreEqual(lambda*Math.Exp(-lambda*x), Exponential.PDF(lambda, x));
             }
             else
             {
                 Assert.AreEqual(0.0, n.Density(lambda));
+                Assert.AreEqual(0.0, Exponential.PDF(lambda, lambda));
             }
         }
 
@@ -302,7 +304,8 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         public void ValidateDensityLn(double lambda, double x)
         {
             var n = new Exponential(lambda);
-            Assert.AreEqual(Math.Log(lambda) - (lambda * x), n.DensityLn(x));
+            Assert.AreEqual(Math.Log(lambda) - (lambda*x), n.DensityLn(x));
+            Assert.AreEqual(Math.Log(lambda) - (lambda*x), Exponential.PDFLn(lambda, x));
         }
 
         /// <summary>
@@ -356,12 +359,34 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
             var n = new Exponential(lambda);
             if (x >= 0.0)
             {
-                Assert.AreEqual(1.0 - Math.Exp(-lambda * x), n.CumulativeDistribution(x));
+                Assert.AreEqual(1.0 - Math.Exp(-lambda*x), n.CumulativeDistribution(x));
+                Assert.AreEqual(1.0 - Math.Exp(-lambda*x), Exponential.CDF(lambda, x));
             }
             else
             {
                 Assert.AreEqual(0.0, n.CumulativeDistribution(x));
+                Assert.AreEqual(0.0, Exponential.CDF(lambda, x));
             }
         }
+
+        /// <summary>
+        /// Validate inverse cumulative distribution.
+        /// </summary>
+        /// <param name="lambda">Lambda value.</param>
+        /// <param name="x">Input X value.</param>
+        [TestCase(0.1, 0.0)]
+        [TestCase(1.0, 0.0)]
+        [TestCase(10.0, 0.0)]
+        [TestCase(10.0, 0.1)]
+        [TestCase(1.0, 1.0)]
+        [TestCase(0.1, Double.PositiveInfinity)]
+        [TestCase(1.0, Double.PositiveInfinity)]
+        [TestCase(10.0, Double.PositiveInfinity)]
+        public void ValidateInverseCumulativeDistribution(double lambda, double x)
+        {
+            var n = new Exponential(lambda);
+            Assert.AreEqual(x, n.InverseCumulativeDistribution(1.0 - Math.Exp(-lambda*x)));
+            Assert.AreEqual(x, Exponential.InvCDF(lambda, 1.0 - Math.Exp(-lambda*x)));
+        }
     }
 }