diff --git a/CHANGELOG b/CHANGELOG
--- a/CHANGELOG
+++ b/CHANGELOG
@@ -1,5 +1,9 @@
 	# Changelog
 
+	- 2.1.0 (2019-07-23)
+	* Generalises 'categorical' and 'multinomial' to take things proportional to
+	  probabilities, rather than probabilities proper.
+
 	- 2.0.4 (2018-06-30)
 	* Clean up docs and add some additional usage information.
 	* Split the existing Student t distribution into 'student' and its
diff --git a/mwc-probability.cabal b/mwc-probability.cabal
--- a/mwc-probability.cabal
+++ b/mwc-probability.cabal
@@ -1,5 +1,5 @@
 name:                mwc-probability
-version:             2.0.4
+version:             2.1.0
 homepage:            http://github.com/jtobin/mwc-probability
 license:             MIT
 license-file:        LICENSE
@@ -8,7 +8,7 @@
 category:            Math
 build-type:          Simple
 cabal-version:       >= 1.10
-tested-with:         GHC == 8.0.2, GHC == 8.2.2 , GHC == 8.4.2
+tested-with:         GHC == 8.0.2, GHC == 8.2.2 , GHC == 8.4.2, GHC == 8.6.5
 synopsis:            Sampling function-based probability distributions.
 description:
 
@@ -55,7 +55,7 @@
   hs-source-dirs:      src
   build-depends:
       base          >=  4.8 && < 6
-    , mwc-random    >   0.13 && < 0.14
+    , mwc-random    >   0.13 && < 0.15
     , primitive     >=  0.6 && < 1.0
     , transformers  >=  0.5 && < 1.0
 
diff --git a/src/System/Random/MWC/Probability.hs b/src/System/Random/MWC/Probability.hs
--- a/src/System/Random/MWC/Probability.hs
+++ b/src/System/Random/MWC/Probability.hs
@@ -340,15 +340,21 @@
 -- | The multinomial distribution of `n` trials and category probabilities
 --   `ps`.
 --
---   Note that `ps` is a vector of probabilities and should sum to one.
+--   Note that the supplied probability container should consist of non-negative
+--   values but is not required to sum to one.
 multinomial :: (Foldable f, PrimMonad m) => Int -> f Double -> Prob m [Int]
 multinomial n ps = do
-  let cumulative = scanl1 (+) (F.toList ps)
-  replicateM n $ do
-    z <- uniform
-    case findIndex (> z) cumulative of
-      Just g  -> return g
-      Nothing -> error "mwc-probability: invalid probability vector"
+    let (cumulative, total) = runningTotals (F.toList ps)
+    replicateM n $ do
+      z <- uniformR (0, total)
+      case findIndex (> z) cumulative of
+        Just g  -> return g
+        Nothing -> error "mwc-probability: invalid probability vector"
+  where
+    -- Note: this is significantly faster than any
+    -- of the recursions one might write by hand.
+    runningTotals :: Num a => [a] -> ([a], a)
+    runningTotals xs = let adds = scanl1 (+) xs in (adds, sum xs)
 {-# INLINABLE multinomial #-}
 
 -- | Generalized Student's t distribution with location parameter `m`, scale
@@ -404,7 +410,8 @@
 
 -- | A categorical distribution defined by the supplied probabilities.
 --
---   Note that the supplied container of probabilities must sum to 1.
+--   Note that the supplied probability container should consist of non-negative
+--   values but is not required to sum to one.
 categorical :: (Foldable f, PrimMonad m) => f Double -> Prob m Int
 categorical ps = do
   xs <- multinomial 1 ps