Cdf of multivariate normal in distributions.jl

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I used HCubature to calculate integral of PDF. Maybe not the fastest, but it works

using HCubature, Distributions, Plots, LinearAlgebra
plotly()
μ = [0.0, 0.0]
Σ = [1.0 0.0; 0.0 1.0]

my_pdf(x) = ((2*pi)^2*det(Σ))^(-0.5)*exp(-0.5*transpose(x-μ)*inv(Σ)*(x-μ))
mv_norm_cdf(x,y)= hcubature(x -> my_pdf(x), [-10.0, -10.0], [x, y])[1]

xs = -5:0.5:5
ys = -5:0.5:5

surface(xs,ys, mv_norm_cdf, xlabel="X", ylabel="Y", zlabel="CDF", color=:viridis, zlim=[0,1])
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