Fix tails of Quantile transform

Author: juliohm

src/distributions.jl

@@ -22,9 +22,9 @@ quantile(d::EmpiricalDistribution, p::Real) = quantile(d.values, p, sorted=true)
 
 function cdf(d::EmpiricalDistribution{T}, x::T) where {T<:Real}
   v = d.values
-  N = length(v)
+  n = length(v)
 
-  head, mid, tail = 1, 1, N
+  head, mid, tail = 1, 1, n
   while tail - head > 1
     mid = (head + tail) ÷ 2
     if x < v[mid]
@@ -37,14 +37,14 @@ function cdf(d::EmpiricalDistribution{T}, x::T) where {T<:Real}
   l, u = v[head], v[tail]
 
   if x < l
-    return 0.
+    return zero(T)
   elseif x > u
-    return 1.
+    return one(T)
   else
     if head == tail
-      return head / N
+      return head / n
     else
-      pl, pu = head / N, tail / N
+      pl, pu = head / n, tail / n
       return (pu - pl) * (x - l) / (u - l) + pl
     end
   end

src/transforms/quantile.jl

@@ -31,8 +31,12 @@ end
 
 # transform samples from original to target distribution
 function qqtransform(samples, origin, target)
+  # avoid evaluating the quantile at 0 or 1
+  T = eltype(samples)
+  low = zero(T) + T(0.001)
+  high = one(T) - T(0.001)
   map(samples) do sample
     prob = cdf(origin, sample)
-    quantile(target, prob - eps())
+    quantile(target, clamp(prob, low, high))
   end
 end

test/transforms.jl

@@ -204,7 +204,11 @@
   end
 
   @testset "Quantile" begin
-    # TODO
+    t = (z=rand(1000),)
+    n, c = apply(Quantile(), t)
+    r = revert(Quantile(), n, c)
+    @test all(-4 .< extrema(n.z) .< 4)
+    @test all(0 .≤ extrema(r.z) .≤ 1)
   end
 
   @testset "Functional" begin