From fa493fb84020b9c8f9449ffeccbc5b0d6c313831 Mon Sep 17 00:00:00 2001
From: David Widmann <devmotion@users.noreply.github.com>
Date: Thu, 30 May 2024 08:58:28 +0200
Subject: [PATCH] Clamp `cdf` and `ccdf` of `Truncated` (#1865)

---
 src/truncate.jl  |  6 ++++--
 test/truncate.jl | 18 ++++++++++++++++++
 2 files changed, 22 insertions(+), 2 deletions(-)

diff --git a/src/truncate.jl b/src/truncate.jl
index 45709f6b5..48d62b015 100644
--- a/src/truncate.jl
+++ b/src/truncate.jl
@@ -166,7 +166,8 @@ function logpdf(d::Truncated, x::Real)
 end
 
 function cdf(d::Truncated, x::Real)
-    result = (cdf(d.untruncated, x) - d.lcdf) / d.tp
+    result = clamp((cdf(d.untruncated, x) - d.lcdf) / d.tp, 0, 1)
+    # Special cases for values outside of the support to avoid e.g. NaN issues with `Binomial`
     return if d.lower !== nothing && x < d.lower
         zero(result)
     elseif d.upper !== nothing && x >= d.upper
@@ -188,7 +189,8 @@ function logcdf(d::Truncated, x::Real)
 end
 
 function ccdf(d::Truncated, x::Real)
-    result = (d.ucdf - cdf(d.untruncated, x)) / d.tp
+    result = clamp((d.ucdf - cdf(d.untruncated, x)) / d.tp, 0, 1)
+    # Special cases for values outside of the support to avoid e.g. NaN issues with `Binomial`
     return if d.lower !== nothing && x <= d.lower
         one(result)
     elseif d.upper !== nothing && x > d.upper
diff --git a/test/truncate.jl b/test/truncate.jl
index b409cba93..9c2a286d0 100644
--- a/test/truncate.jl
+++ b/test/truncate.jl
@@ -214,3 +214,21 @@ end
 
   @test isa(quantile(d, ForwardDiff.Dual(1.,0.)), ForwardDiff.Dual)
 end
+
+@testset "cdf outside of [0, 1] (#1854)" begin
+    dist = truncated(Normal(2.5, 0.2); lower=0.0)
+    @test @inferred(cdf(dist, 3.741058503233821e-17)) === 0.0
+    @test @inferred(ccdf(dist, 3.741058503233821e-17)) === 1.0
+    @test @inferred(cdf(dist, 1.4354474178676617e-18)) === 0.0
+    @test @inferred(ccdf(dist, 1.4354474178676617e-18)) === 1.0
+    @test @inferred(cdf(dist, 8.834854780587132e-18)) === 0.0
+    @test @inferred(ccdf(dist, 8.834854780587132e-18)) === 1.0
+
+    dist = truncated(
+        Normal(2.122039143928797, 0.07327367710864985);
+        lower = 1.9521656132878236,
+        upper = 2.8274429454898398,
+    )
+    @test @inferred(cdf(dist, 2.82)) === 1.0
+    @test @inferred(ccdf(dist, 2.82)) === 0.0
+end