Try #612:

Project.toml

@@ -22,6 +22,7 @@ Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 Requires = "ae029012-a4dd-5104-9daa-d747884805df"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 TimerOutputs = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
+Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
 [compat]
 AbstractFFTs = "0.4, 0.5"

src/CuArrays.jl

@@ -94,6 +94,7 @@ include("accumulate.jl")
 include("linalg.jl")
 include("nnlib.jl")
 include("iterator.jl")
+include("statistics.jl")
 
 include("deprecated.jl")
 

src/statistics.jl

@@ -0,0 +1,13 @@
+import Statistics
+
+Statistics._var(A::CuArray, corrected::Bool, mean, dims) =
+    sum((A .- something(mean, Statistics.mean(A, dims=dims))).^2, dims=dims)/(prod(size(A)[[dims...]])-corrected)
+
+Statistics._var(A::CuArray, corrected::Bool, mean, ::Colon) = 
+    sum((A .- something(mean, Statistics.mean(A))).^2)/(length(A)-corrected)
+
+Statistics._std(A::CuArray, corrected::Bool, mean, dims) =
+    sqrt.(Statistics.var(A; corrected=corrected, mean=mean, dims=dims))
+
+Statistics._std(A::CuArray, corrected::Bool, mean, ::Colon) =
+    sqrt.(Statistics.var(A; corrected=corrected, mean=mean, dims=:))

test/runtests.jl

@@ -64,6 +64,7 @@ include("iterator.jl")
 
 include("forwarddiff.jl")
 include("nnlib.jl")
+include("statistics.jl")
 
 if haskey(ENV, "CI")
   CuArrays.memory_status()

test/statistics.jl

@@ -0,0 +1,18 @@
+@testset "Statistics" begin
+
+using Statistics
+
+@testset "std" begin
+    @test testf(std, rand(10))
+    @test testf(std, rand(10,1,2))
+    @test testf(std, rand(10,1,2), corrected=true)
+    @test testf(std, rand(10,1,2), dims=1)
+end
+@testset "var" begin
+    @test testf(var, rand(10))
+    @test testf(var, rand(10,1,2))
+    @test testf(var, rand(10,1,2), corrected=true)
+    @test testf(var, rand(10,1,2), dims=1)
+end
+
+end