From 2c78ee93fdefd4d9dc2760d2d3ae6ef31b4ad23b Mon Sep 17 00:00:00 2001
From: Richard Reeve <git@richardreeve.net>
Date: Fri, 31 Jul 2015 16:49:48 +0100
Subject: [PATCH 1/2] Allow for rate to be 0 in Poisson distribution,
 everything worked already except entropy (which is corrected to 0) and
 maximum (which is corrected to 0).

---
 src/univariate/discrete/poisson.jl | 8 +++++---
 1 file changed, 5 insertions(+), 3 deletions(-)

diff --git a/src/univariate/discrete/poisson.jl b/src/univariate/discrete/poisson.jl
index c0edc5867..20b861e83 100644
--- a/src/univariate/discrete/poisson.jl
+++ b/src/univariate/discrete/poisson.jl
@@ -2,7 +2,7 @@ immutable Poisson <: DiscreteUnivariateDistribution
     λ::Float64
 
     function Poisson(λ::Float64)
-        λ > 0.0 || error("λ must be positive.")
+        λ >= 0.0 || error("λ must be non-negative.")
         new(λ)
     end
 
@@ -10,7 +10,7 @@ immutable Poisson <: DiscreteUnivariateDistribution
     Poisson() = new(1.0)
 end
 
-@distr_support Poisson 0 Inf
+@distr_support Poisson 0 (d.λ == 0.0 ? 0 : Inf)
 
 
 ### Parameters
@@ -39,7 +39,9 @@ kurtosis(d::Poisson) = 1.0 / d.λ
 
 function entropy(d::Poisson)
     λ = rate(d)
-    if λ < 50.0
+    if λ == 0.0
+        return 0.0
+    elseif λ < 50.0
         s = 0.0
         λk = 1.0
         for k = 1:100

From 9e8cfb420e194b61d502bf1a14dec8dd79d8da23 Mon Sep 17 00:00:00 2001
From: Richard Reeve <git@richardreeve.net>
Date: Fri, 31 Jul 2015 16:50:08 +0100
Subject: [PATCH 2/2] Add tests for Poisson(0.0) distribution.

---
 test/discrete_test.json | 27 +++++++++++++++++++++++++++
 1 file changed, 27 insertions(+)

diff --git a/test/discrete_test.json b/test/discrete_test.json
index bb5a65b21..9f1d9447e 100644
--- a/test/discrete_test.json
+++ b/test/discrete_test.json
@@ -1375,6 +1375,33 @@
       "var": 1.0
     }
   ], 
+  [
+    "Poisson(0.0)", 
+    {
+      "dtype": "Poisson", 
+        "entropy": 0.0,
+      "maximum": 0, 
+      "mean": 0.0, 
+      "median": 0.0, 
+      "minimum": 0, 
+      "params": {
+        "rate": 0.0
+      }, 
+      "points": [
+        {
+          "cdf": 1.0, 
+          "logpdf": 0.0, 
+          "x": 0
+        }
+      ], 
+      "q10": 0.0, 
+      "q25": 0.0, 
+      "q50": 0.0, 
+      "q75": 0.0, 
+      "q90": 0.0, 
+      "var": 0.0
+    }
+  ], 
   [
     "Poisson(0.5)", 
     {