diff --git a/Project.toml b/Project.toml
index 661aaf6e..d5ff8381 100644
--- a/Project.toml
+++ b/Project.toml
@@ -26,12 +26,13 @@ Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
 Static = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
+StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Tricks = "410a4b4d-49e4-4fbc-ab6d-cb71b17b3775"
 
 [compat]
 ChainRulesCore = "1"
-ChangesOfVariables = "0.1.3"
+ChangesOfVariables = "0.1"
 Compat = "3.35, 4"
 ConstructionBase = "1.3"
 DensityInterface = "0.4"
@@ -52,6 +53,7 @@ Reexport = "1"
 SpecialFunctions = "2"
 Static = "0.8, 1"
 Statistics = "1"
+StatsBase = "0.34"
 Test = "1"
 Tricks = "0.1"
 julia = "1.6"
diff --git a/src/rand.jl b/src/rand.jl
index f92cb16a..db5a31cd 100644
--- a/src/rand.jl
+++ b/src/rand.jl
@@ -8,6 +8,24 @@ Base.rand(rng::AbstractRNG, d::AbstractMeasure) = rand(rng, Float64, d)
 
 @inline Random.rand!(d::AbstractMeasure, args...) = rand!(GLOBAL_RNG, d, args...)
 
+@inline function Base.rand(
+    rng::AbstractRNG,
+    ::Type{T},
+    d::ProductMeasure{A},
+) where {T,A<:AbstractArray}
+    mar = marginals(d)
+
+    # Distributions doens't (yet) have the three-argument form
+    elT = typeof(rand(rng, T, first(mar)))
+
+    sz = size(mar)
+    x = Array{elT,length(sz)}(undef, sz)
+    @inbounds @simd for j in eachindex(mar)
+        x[j] = rand(rng, T, mar[j])
+    end
+    x
+end
+
 # TODO: Make this work
 # function Base.rand(rng::AbstractRNG, ::Type{T}, d::AbstractMeasure) where {T}
 #     x = testvalue(d)
diff --git a/src/utils.jl b/src/utils.jl
index d0f85481..2d294b37 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -164,3 +164,12 @@ using InverseFunctions: FunctionWithInverse
 
 unwrap(f) = f
 unwrap(f::FunctionWithInverse) = f.f
+
+import Statistics
+import StatsBase
+
+StatsBase.entropy(m::AbstractMeasure, b::Real) = entropy(proxy(m), b)
+Statistics.mean(m::AbstractMeasure) = mean(proxy(m))
+Statistics.std(m::AbstractMeasure) = std(proxy(m))
+Statistics.var(m::AbstractMeasure) = var(proxy(m))
+Statistics.quantile(m::AbstractMeasure, q) = quantile(proxy(m), q)
\ No newline at end of file