More tests based on the original paper

test/methods/correlation/azadkia_chatterjee_coefficient.jl

@@ -1,4 +1,5 @@
 using Test
+using Statistics
 using Random
 rng = Xoshiro(12345)
 n = 15
@@ -8,6 +9,22 @@ z = rand(rng, n)
 m = AzadkiaChatterjeeCoefficient()
 @test association(m, x, y) isa Real
 @test association(m, x, y, z) isa Real
+
+# Example 8.2 from Azadkia & Chatterjee.
+# We're doing 10 replicates and seeing if the mean Tₙ(Y, Z | X₁) and Tₙ(Y, Z) is within the 
+# range of values they get.
+Tₙs_cond = zeros(10)
+Tₙs_pairwise = zeros(10)
+
+m = AzadkiaChatterjeeCoefficient()
+for i = 1:10
+    n = 1000; x1, x2 = randn(n), randn(n); y = x1 .^2 .+ x2 .^ 2; z = atan.(x1 ./ x2)
+    Tₙs_cond[i] = association(m, y, z, x1)
+    Tₙs_pairwise[i] = association(m, y, z)
+end
+@test all(0.79 < mean(Tₙs_cond) < 0.84)
+@test all(-0.06 < mean(Tₙs_pairwise) < 0.06)
+
 # pretty printing
 out = repr(AzadkiaChatterjeeCoefficient())
 @test occursin("AzadkiaChatterjeeCoefficient", out)