diff --git a/Statistics/Distribution/Poisson.hs b/Statistics/Distribution/Poisson.hs
--- a/Statistics/Distribution/Poisson.hs
+++ b/Statistics/Distribution/Poisson.hs
@@ -31,15 +31,18 @@
 import Data.Binary          (Binary(..))
 import Data.Data            (Data, Typeable)
 import GHC.Generics         (Generic)
+
+import qualified System.Random.MWC.Distributions as MWC
+
 import Numeric.SpecFunctions (incompleteGamma,logFactorial)
 import Numeric.MathFunctions.Constants (m_neg_inf)
 
+
 import qualified Statistics.Distribution as D
 import qualified Statistics.Distribution.Poisson.Internal as I
 import Statistics.Internal
 
 
-
 newtype PoissonDistribution = PD {
       poissonLambda :: Double
     } deriving (Eq, Typeable, Data, Generic)
@@ -92,6 +95,14 @@
 
 instance D.MaybeEntropy PoissonDistribution where
   maybeEntropy = Just . D.entropy
+
+-- | @since 0.16.5.0
+instance D.DiscreteGen PoissonDistribution where
+  genDiscreteVar (PD lambda) = MWC.poisson lambda
+
+-- | @since 0.16.5.0
+instance D.ContGen PoissonDistribution where
+  genContVar (PD lambda) gen = fromIntegral <$> MWC.poisson lambda gen
 
 -- | Create Poisson distribution.
 poisson :: Double -> PoissonDistribution
diff --git a/changelog.md b/changelog.md
--- a/changelog.md
+++ b/changelog.md
@@ -1,3 +1,8 @@
+## Changes in 0.16.5.0 [2026.01.09]
+
+ * `ContGen` and `DiscreteGen` instances for `Poisson` distributions are added.
+
+
 ## Changes in 0.16.4.0 [2025.10.23]
 
  * Bartlett's test (`Statistics.Test.Bartlett`) and Levene's test
diff --git a/statistics.cabal b/statistics.cabal
--- a/statistics.cabal
+++ b/statistics.cabal
@@ -2,7 +2,7 @@
 build-type:     Simple
 
 name:           statistics
-version:        0.16.4.0
+version:        0.16.5.0
 synopsis:       A library of statistical types, data, and functions
 description:
   This library provides a number of common functions and types useful
@@ -128,7 +128,7 @@
   build-depends: base                    >= 4.9 && < 5
                  --
                , math-functions          >= 0.3.4.1
-               , mwc-random              >= 0.15.0.0
+               , mwc-random              >= 0.15.3.0
                , random                  >= 1.2
                  --
                , aeson                   >= 0.6.0.0