diff --git a/basis/random/random-tests.factor b/basis/random/random-tests.factor
index 3fc4ff80eb..fc545a9247 100644
--- a/basis/random/random-tests.factor
+++ b/basis/random/random-tests.factor
@@ -1,5 +1,5 @@
 USING: random sequences tools.test kernel math math.functions
-sets grouping random.private ;
+sets grouping random.private math.statistics ;
 IN: random.tests
 
 [ 4 ] [ 4 random-bytes length ] unit-test
@@ -33,3 +33,15 @@ IN: random.tests
 
 [ ]
 [ [ 100 random-bytes ] with-system-random drop ] unit-test
+
+{ t }
+[ 50000 [ .15 exponential-random-float ] replicate [ mean ] [ std ] bi .2 ~ ] unit-test
+
+{ t }
+[ 50000 [ 1 exponential-random-float ] replicate [ mean ] [ std ] bi .2 ~ ] unit-test
+
+{ t t }
+[
+    50000 [ 1 3 pareto-random-float ] replicate [ mean ] [ std ] bi
+    [ 1.5 .3 ~ ] [ 3 sqrt 2 / .3 ~ ] bi*
+] unit-test
diff --git a/basis/random/random.factor b/basis/random/random.factor
index 4c69437244..107c090afd 100644
--- a/basis/random/random.factor
+++ b/basis/random/random.factor
@@ -127,8 +127,8 @@ ERROR: too-many-samples seq n ;
         1. swap / ^
     ] dip * ;
 
-: pareto-random-float ( alpha -- n )
-    [ random-unit ] dip [ 1. swap / ] bi@ ^ ;
+: pareto-random-float ( k alpha -- n )
+    [ random-unit ] dip recip ^ /f ;
 
 :: (gamma-random-float>1) ( alpha beta -- n )
     ! Uses R.C.H. Cheng, "The generation of Gamma