Re-write median(Binomial) to improve speed

src/univariate/discrete/binomial.jl

@@ -73,6 +73,24 @@ function mode(d::Binomial{T}) where T<:Real
 end
 modes(d::Binomial) = Int[mode(d)]
 
+function median(dist::Binomial)
+    bound = min(dist.p, 1-dist.p) # from http://dx.doi.org/10.1111/j.1467-9574.1980.tb00681.x
+    dist_mean = mean(dist)
+
+    floor_mean = floor(Int, dist_mean)
+    difference = dist_mean - floor_mean
+
+    if difference <= bound
+        floor_mean
+    elseif  difference >= 1 - bound
+        floor_mean + 1
+    elseif cdf(dist, floor_mean) >= 0.5
+        floor_mean
+    else
+        floor_mean + 1
+    end
+end
+
 function skewness(d::Binomial)
     n, p1 = params(d)
     p0 = 1 - p1

test/univariate/discrete/binomial.jl

@@ -32,7 +32,11 @@ end
 @test median(Binomial(45,3//10)) == 13
 @test median(Binomial(65,3//10)) == 19
 @test median(Binomial(85,3//10)) == 25
-
+
+@test median(Binomial(25,0.756)) == 19
+@test median(Binomial(25,1//2)) == 12
+@test median(Binomial(25,3//5)) == 15
+
 # Test mode
 @test Distributions.mode(Binomial(100, 0.4)) == 40
 @test Distributions.mode(Binomial(1, 0.51)) == 1