Clean up cdf functions

* For discrete functions with finite support, calculate
  cdf from right if we're in the right half of that support
* Remove cdf specialized on BetaBinomial (handled by
  DiscreteUnivariateDistribution version)

src/univariate/discrete/betabinomial.jl

@@ -70,19 +70,3 @@ mode(d::BetaBinomial) = indmax(pdf(d)) - 1
 modes(d::BetaBinomial) = [x - 1 for x in modes(Categorical(pdf(d)))]
 
 quantile(d::BetaBinomial, p::Float64) = quantile(Categorical(pdf(d)), p) - 1
-
-function cdf(d::BetaBinomial, x::Int)
-  c = 0.0
-  for y = minimum(d):min(floor(Int,x), maximum(d))
-    c += pdf(d, y)
-  end
-
-  # TODO: remove when https://github.com/JuliaLang/julia/issues/14620 is resolved
-  # this is needed due to the fact that pdf(d, y) can return values that are imprecise at higher decimal places (due to https://github.com/JuliaLang/julia/issues/14620)
-  # and so due to the impl above we can end up with cdf values that are basically 1 but are either slightly greater or smaller
-  if abs(c - 1.0) < 1.0e-10
-    c = 1.0
-  end
-
-  return c
-end

src/univariates.jl

@@ -37,6 +37,10 @@ end
 @compat support{D<:ContinuousUnivariateDistribution}(d::Union{D,Type{D}}) = RealInterval(minimum(d), maximum(d))
 @compat support{D<:DiscreteUnivariateDistribution}(d::Union{D,Type{D}}) = round(Int, minimum(d)):round(Int, maximum(d))
 
+# Type used for dispatch on finite support
+# T = true or false
+immutable FiniteSupport{T} end
+
 ## macros to declare support
 
 macro distr_support(D, lb, ub)
@@ -108,15 +112,31 @@ logpdf(d::ContinuousUnivariateDistribution, x::Float64) = log(pdf(d, x))
 @compat logpdf(d::ContinuousUnivariateDistribution, x::Real) = logpdf(d, Float64(x))
 
 # cdf
+cdf(d::DiscreteUnivariateDistribution, x::Int) = cdf(d, x, FiniteSupport{hasfinitesupport(d)})
 
-function cdf(d::DiscreteUnivariateDistribution, x::Int)
+# Discrete univariate with infinite support
+function cdf(d::DiscreteUnivariateDistribution, x::Int, ::Type{FiniteSupport{false}})
     c = 0.0
-    for y = minimum(d):floor(Int,x)
+    for y = minimum(d):x
         c += pdf(d, y)
     end
     return c
 end
 
+# Discrete univariate with finite support
+function cdf(d::DiscreteUnivariateDistribution, x::Int, ::Type{FiniteSupport{true}})
+    # calculate from left if x < (min + max)/2
+    # (same as infinite support version)
+    x <= div(minimum(d) + maximum(d),2) && return cdf(d, x, FiniteSupport{false})
+
+    # otherwise, calculate from the right
+    c = 1.0
+    for y = x+1:maximum(d)
+        c -= pdf(d, y)
+    end
+    return c
+end
+
 cdf(d::DiscreteUnivariateDistribution, x::Real) = cdf(d, floor(Int,x))
 
 cdf(d::ContinuousUnivariateDistribution, x::Float64) = throw(MethodError(cdf, (d, x)))