diff --git a/EpiAware/src/EpiAwareUtils/EpiAwareUtils.jl b/EpiAware/src/EpiAwareUtils/EpiAwareUtils.jl
index bcabad2d0..af0bab2f4 100644
--- a/EpiAware/src/EpiAwareUtils/EpiAwareUtils.jl
+++ b/EpiAware/src/EpiAwareUtils/EpiAwareUtils.jl
@@ -10,11 +10,13 @@ using DynamicPPL: Model, fix, condition, @submodel, @model
 using MCMCChains: Chains
 using Random: AbstractRNG, randexp
 using Tables: rowtable
+import Base: eltype
 
 using Distributions, DocStringExtensions, QuadGK, Statistics, Turing
 
 #Export Structures
-export HalfNormal, DirectSample, SafePoisson, SafeNegativeBinomial
+export HalfNormal, DirectSample, SafePoisson, SafeNegativeBinomial, RealValued,
+       RealUnivariateDistribution
 
 #Export functions
 export scan, spread_draws, censored_cdf, censored_pmf, get_param_array, prefix_submodel, ∫F
@@ -32,6 +34,7 @@ include("turing-methods.jl")
 include("DirectSample.jl")
 include("post-inference.jl")
 include("get_param_array.jl")
+include("RealValued.jl")
 include("SafePoisson.jl")
 include("SafeNegativeBinomial.jl")
 
diff --git a/EpiAware/src/EpiAwareUtils/RealValued.jl b/EpiAware/src/EpiAwareUtils/RealValued.jl
new file mode 100644
index 000000000..9b5c4c462
--- /dev/null
+++ b/EpiAware/src/EpiAwareUtils/RealValued.jl
@@ -0,0 +1,12 @@
+"""
+A type to represent real-valued distributions, the purpose of this type is to avoid problems
+with the `eltype` function when having `rand` calls in the model.
+"""
+struct RealValued <: Distributions.ValueSupport end
+Base.eltype(::Type{<:Distributions.Sampleable{F, RealValued}}) where {F} = Real
+
+"""
+A constant alias for `Distribution{Univariate, RealValued}`. This type represents a univariate distribution with real-valued outcomes.
+"""
+const RealUnivariateDistribution = Distributions.Distribution{
+    Distributions.Univariate, RealValued}
diff --git a/EpiAware/src/EpiAwareUtils/SafeNegativeBinomial.jl b/EpiAware/src/EpiAwareUtils/SafeNegativeBinomial.jl
index 4341bcc28..010cdb0ac 100644
--- a/EpiAware/src/EpiAwareUtils/SafeNegativeBinomial.jl
+++ b/EpiAware/src/EpiAwareUtils/SafeNegativeBinomial.jl
@@ -65,7 +65,7 @@ var(d)
 2.4617291430060293e40
 ```
 "
-struct SafeNegativeBinomial{T <: Real} <: DiscreteUnivariateDistribution
+struct SafeNegativeBinomial{T <: Real} <: RealUnivariateDistribution
     r::T
     p::T
 
diff --git a/EpiAware/src/EpiAwareUtils/SafePoisson.jl b/EpiAware/src/EpiAwareUtils/SafePoisson.jl
index 46e5201ad..0ec1122b9 100644
--- a/EpiAware/src/EpiAwareUtils/SafePoisson.jl
+++ b/EpiAware/src/EpiAwareUtils/SafePoisson.jl
@@ -45,7 +45,7 @@ var(d)
 7.016735912097631e20
 ```
 "
-struct SafePoisson{T <: Real} <: DiscreteUnivariateDistribution
+struct SafePoisson{T <: Real} <: RealUnivariateDistribution
     λ::T
 
     SafePoisson{T}(λ::Real) where {T <: Real} = new{T}(λ)
@@ -86,7 +86,7 @@ Distributions.rate(d::SafePoisson) = d.λ
 ### Statistics
 
 Distributions.mean(d::SafePoisson) = d.λ
-Distributions.mode(d::SafePoisson) = _safe_int_floor(d.λ)
+Distributions.mode(d::SafePoisson) = floor(d.λ)
 Distributions.var(d::SafePoisson) = d.λ
 Distributions.skewness(d::SafePoisson) = one(typeof(d.λ)) / sqrt(d.λ)
 Distributions.kurtosis(d::SafePoisson) = one(typeof(d.λ)) / d.λ
@@ -142,12 +142,12 @@ ad_rand(λ) = ad_rand(Random.GLOBAL_RNG, λ)
 function ad_rand(rng::AbstractRNG, λ)
     s = sqrt(λ)
     d = 6.0 * λ^2
-    L = _safe_int_floor(λ - 1.1484)
+    L = floor(λ - 1.1484)
     # Step N
     G = λ + s * randn(rng)
 
     if G >= 0.0
-        K = _safe_int_floor(G)
+        K = floor(G)
         # Step I
         if K >= L
             return K
@@ -177,7 +177,7 @@ function ad_rand(rng::AbstractRNG, λ)
             continue
         end
 
-        K = _safe_int_floor(λ + s * T)
+        K = floor(λ + s * T)
         px, py, fx, fy = procf(λ, K, s)
         c = 0.1069 / λ
 
@@ -229,7 +229,7 @@ function log1pmx(x::Float64)
 end
 
 # Procedure F
-function procf(λ, K::Int, s::Float64)
+function procf(λ, K, s::Float64)
     # can be pre-computed, but does not seem to affect performance
     ω = 0.3989422804014327 / s
     b1 = 0.041666666666666664 / λ
@@ -241,7 +241,7 @@ function procf(λ, K::Int, s::Float64)
 
     if K < 10
         px = -float(λ)
-        py = λ^K / factorial(K)
+        py = λ^K / factorial(floor(Int, K))
     else
         δ = 0.08333333333333333 / K
         δ -= 4.8 * δ^3
diff --git a/EpiAware/test/EpiAwareUtils/RealValued.jl b/EpiAware/test/EpiAwareUtils/RealValued.jl
new file mode 100644
index 000000000..13205084d
--- /dev/null
+++ b/EpiAware/test/EpiAwareUtils/RealValued.jl
@@ -0,0 +1,8 @@
+@testitem "RealValued Type Tests" begin
+    using Distributions
+    struct DummySampleable <: Sampleable{Univariate, RealValued} end
+
+    @test RealValued <: Distributions.ValueSupport
+    @test eltype(DummySampleable) == Real
+    @test RealUnivariateDistribution == Distribution{Univariate, RealValued}
+end
diff --git a/EpiAware/test/EpiAwareUtils/SafeNegativeBinomial.jl b/EpiAware/test/EpiAwareUtils/SafeNegativeBinomial.jl
index 8c828e49d..7e5bb98cd 100644
--- a/EpiAware/test/EpiAwareUtils/SafeNegativeBinomial.jl
+++ b/EpiAware/test/EpiAwareUtils/SafeNegativeBinomial.jl
@@ -70,7 +70,7 @@ end
 
     dist = SafeNegativeBinomial(r, p)
     @testset "Large value of mean samples a BigInt with SafePoisson" begin
-        @test rand(dist) isa BigInt
+        @test rand(dist) isa Real
     end
     @testset "Large value of mean sample failure with Poisson" begin
         _dist = EpiAware.EpiAwareUtils._negbin(dist)
diff --git a/EpiAware/test/EpiAwareUtils/SafePoisson.jl b/EpiAware/test/EpiAwareUtils/SafePoisson.jl
index 6630e066b..e4f889254 100644
--- a/EpiAware/test/EpiAwareUtils/SafePoisson.jl
+++ b/EpiAware/test/EpiAwareUtils/SafePoisson.jl
@@ -2,9 +2,9 @@
     λ = 10.0
     dist = SafePoisson(λ)
     @test typeof(dist) <: SafePoisson
-    @test rand(dist) isa Int
-    @test rand(dist, 10) isa Vector{Int}
-    @test rand(dist, 10, 10) isa Array{Int}
+    @test rand(dist) isa Real
+    @test rand(dist, 10) isa Vector{Real}
+    @test rand(dist, 10, 10) isa Array{Real}
 end
 
 @testitem "Check distribution properties of SafePoisson" begin
@@ -54,7 +54,7 @@ end
     bigλ = exp(48.0) #Large value of λ
     dist = SafePoisson(bigλ)
     @testset "Large value of mean samples a BigInt with SafePoisson" begin
-        @test rand(dist) isa BigInt
+        @test rand(dist) isa Real
     end
     @testset "Large value of mean sample failure with Poisson" begin
         _dist = Poisson(dist.λ)
diff --git a/EpiAware/test/EpiObsModels/modifiers/PrefixObservationModel.jl b/EpiAware/test/EpiObsModels/modifiers/PrefixObservationModel.jl
index b46ba54c4..346d2b9ba 100644
--- a/EpiAware/test/EpiObsModels/modifiers/PrefixObservationModel.jl
+++ b/EpiAware/test/EpiObsModels/modifiers/PrefixObservationModel.jl
@@ -10,5 +10,5 @@ end
 
     mdl = generate_observations(model, missing, 10)
     draw = rand(mdl)
-    @test typeof(draw[:var"Test.y_t[1]"]) <: Int
+    @test typeof(draw[:var"Test.y_t[1]"]) <: Real
 end