added tests for D'Agostino test for skewness

Updated docs for D'Agostino test

added test, plus code formatting

docs/src/parametric.md

@@ -56,3 +56,8 @@ LeveneTest
 ```@docs
 BrownForsytheTest
 ```
+
+## D'Agostino Test
+```@docs
+AgostinoTest
+```

src/agostino_test.jl

@@ -10,14 +10,13 @@ end
 
 
 function agostino_stat(x::AbstractVector{<:Real})
-
-    #x = sort(x)
+
     n = length(x)
 
     if n < 8 || n > 46340
         throw(ArgumentError("Sample size must be ≥ 8 and ≤ 46340"))
     end
-    
+
     g₁ = skewness(x)
     Y = g₁ * sqrt((n + 1) * (n + 3) / (6 * (n - 2)))
     β₂ = 3 * (n^2 + 27 * n - 70) * (n + 1) * (n + 3) / ((n - 2) * (n + 5) * (n + 7) * (n + 9))
@@ -26,7 +25,7 @@ function agostino_stat(x::AbstractVector{<:Real})
     α = sqrt(2 / (W² - 1))
     Z = δ * log(Y / α + sqrt((Y / α)^2 + 1))
 
-    return (n, g₁, Z)    
+    return (n, g₁, Z)
 end
 
 
@@ -41,7 +40,7 @@ D'Agostino, R.B. (1970). Transformation to Normality of the Null Distribution of
 Implements: [`pvalue`](@ref)
 """
 function AgostinoTest(x::AbstractVector{<:Real})
-    AgostinoTest(agostino_stat(x)...)    
+    return AgostinoTest(agostino_stat(x)...)
 end
 
 
@@ -60,18 +59,17 @@ StatsAPI.nobs(x::AgostinoTest) = x.nobs
 function StatsAPI.pvalue(x::AgostinoTest; tail = :both)
 
     check_tail(tail)
-    
+
     left_tail = cdf(Normal(), x.z_statistic)
     right_tail = ccdf(Normal(), x.z_statistic)
-    
+
     if tail == :both
         p = minimum(2 * [left_tail, right_tail])
     elseif tail == :left
         p = left_tail
-    else tail == :right
+    else
         p = right_tail
     end
 
     return p
 end
-

test/agostino_test.jl

@@ -0,0 +1,23 @@
+using HypothesisTests, Test
+
+@testset "D'Agostino Test" begin
+    # Check errors
+    @test_throws ArgumentError AgostinoTest(rand(5))     # too few samples
+    @test_throws ArgumentError AgostinoTest(rand(50000)) # too many samples
+
+    # Check correctness of results (benchmarked against `moments` package in R)
+    y = [
+        2.44816, 1.086045, 0.154618, 0.778503, 0.923376,
+        1.18671, -0.495009, -0.151178, 1.662281, 2.615421,
+    ]
+
+    result = @inferred AgostinoTest(y)
+    @test result.z_statistic ≈ 0.28356 atol = 1.0e-6
+    @test result.skewness ≈ 0.158581 atol = 1.0e-6
+    @test nobs(result) == 10
+    @test pvalue(result) ≈ 0.776748 atol = 1.0e-6
+    @test pvalue(result, tail = :left) ≈ 0.611626 atol = 1.0e-6
+    @test pvalue(result, tail = :right) ≈ 0.388374 atol = 1.0e-6
+    @test AgostinoTest(exp.(y)).z_statistic ≈ 2.10965 atol = 1.0e-5
+    @test AgostinoTest(-1 .* exp.(y)).z_statistic ≈ -2.10965 atol = 1.0e-5
+end

test/runtests.jl

@@ -12,6 +12,7 @@ macro test_ci_approx(x::Expr, y::Expr)
     end
 end
 
+include("agostino_test.jl")
 include("anderson_darling.jl")
 include("augmented_dickey_fuller.jl")
 include("bartlett.jl")