diff --git a/src/univariates.jl b/src/univariates.jl
index c75c579d5b..f0b9920877 100644
--- a/src/univariates.jl
+++ b/src/univariates.jl
@@ -646,7 +646,7 @@ macro _delegate_statsfuns(D, fpre, psyms...)
     pargs = [Expr(:(.), :d, Expr(:quote, s)) for s in psyms]
 
     # output type of `quantile` etc.
-    T = :($D isa DiscreteUnivariateDistribution ? Int : Real)
+    T = :($D <: DiscreteUnivariateDistribution ? Int : Real)
 
     return quote
         $Distributions.pdf(d::$D, x::Real) = $(fpdf)($(pargs...), x)
diff --git a/test/univariates.jl b/test/univariates.jl
index 8913b3866f..4fa2fadc90 100644
--- a/test/univariates.jl
+++ b/test/univariates.jl
@@ -166,3 +166,12 @@ for c in ["discrete",
     verify_and_test_drive(jsonfile, ARGS, 10^6)
     println()
 end
+
+# #1358
+@testset "Poisson quantile" begin
+    d = Poisson(1)
+    @test quantile(d, 0.2) isa Int
+    @test cquantile(d, 0.4) isa Int
+    @test invlogcdf(d, log(0.2)) isa Int
+    @test invlogccdf(d, log(0.6)) isa Int
+end