Fix #894 Normal distribution and its type parameter (#896)

* Partially fixes #894, the `rand` return value type matches the normal type parameter

* Fixes #894, return an appropriate (matching) `eltype` for Normal

* Add tests

src/univariate/continuous/normal.jl

@@ -61,6 +61,8 @@ params(d::Normal) = (d.μ, d.σ)
 location(d::Normal) = d.μ
 scale(d::Normal) = d.σ
 
+eltype(::Normal{T}) where {T} = T
+
 #### Statistics
 
 mean(d::Normal) = d.μ
@@ -87,7 +89,7 @@ cf(d::Normal, t::Real) = exp(im * t * d.μ - d.σ^2/2 * t^2)
 
 #### Sampling
 
-rand(rng::AbstractRNG, d::Normal) = d.μ + d.σ * randn(rng)
+rand(rng::AbstractRNG, d::Normal{T}) where {T} = d.μ + d.σ * randn(rng, T)
 
 
 #### Fitting

test/continuous.jl

@@ -26,6 +26,21 @@ using ForwardDiff
 @test derivative(t -> logpdf(Normal(1.0, 0.15), t), 2.5) ≈ -66.66666666666667
 @test derivative(t -> pdf(Normal(t, 1.0), 0.0), 0.0) == 0.0
 
+# issue #894:
+@testset "Normal distribution with non-standard (ie not Float64) parameter types" begin
+    n32 = Normal(1f0, 0.1f0)
+    n64 = Normal(1., 0.1)
+    nbig = Normal(big(pi), big(ℯ))
+
+    @test eltype(n32) === Float32
+    @test eltype(rand(n32)) === Float32
+    @test eltype(rand(n32, 4)) === Float32
+
+    @test eltype(n64) === Float64
+    @test eltype(rand(n64)) === Float64
+    @test eltype(rand(n64, 4)) === Float64
+end
+
 # Test for numerical problems
 @test pdf(Logistic(6,0.01),-2) == 0