diff --git a/python/pyspark/rddsampler.py b/python/pyspark/rddsampler.py
index 5928b1d892de0..9e7acc28e99dd 100644
--- a/python/pyspark/rddsampler.py
+++ b/python/pyspark/rddsampler.py
@@ -17,6 +17,7 @@
 
 import sys
 import random
+import math
 
 
 class RDDSamplerBase(object):
@@ -37,16 +38,21 @@ def getUniformSample(self):
         return self._random.random()
 
     def getPoissonSample(self, mean):
-        # here we simulate drawing numbers n_i ~ Poisson(lambda = 1/mean) by
-        # drawing a sequence of numbers delta_j ~ Exp(mean)
-        num_arrivals = 0
-        cur_time = self._random.expovariate(mean)
-
-        while cur_time < 1.0:
-            cur_time += self._random.expovariate(mean)
-            num_arrivals += 1
-
-        return num_arrivals
+        # Using Knuth's algorithm described in http://en.wikipedia.org/wiki/Poisson_distribution
+        if mean < 20.0:  # one exp and k+1 random calls
+            l = math.exp(-mean)
+            p = self._random.random()
+            k = 0
+            while p > l:
+                k += 1
+                p *= self._random.random()
+        else:  # switch to the log domain, k+1 expovariate (random + log) calls
+            p = self._random.expovariate(mean)
+            k = 0
+            while p < 1.0:
+                k += 1
+                p += self._random.expovariate(mean)
+        return k
 
     def func(self, split, iterator):
         raise NotImplementedError