```julia using Distributions

μ = Normal(0, 1) ν = Normal(2, 2)

using Roots

cdfdiff = (x -> cdf(μ, x) - cdf(ν, x)) cdfzeros = find_zeros(cdfdiff, -5, 5)

function optimalf(x)

   return 0.5 - 0.1*abs(x-cdfzeros[1])

end

function optimalD(x)

   return 0.4 * pdf(ν, x)/(pdf(μ, x) + pdf(ν, x))

end

function logminusoptimalD(x)

   return log(1-optimalD(x))+0.6

end

using StatsPlots using LaTeXStrings

p1 = plot(μ; label="Generator's distribution") plot!(ν; label="reference distribution")

1. plot!(cdfdiff; linestyle=:dashdot, label=L"CDF_{\mu} - CDF_{\nu}")

vline!(cdfzeros; linestyle=:dashdot, label="equal CDF") plot!(optimalf;label="optimal Wasserstein critic (scaled)") plot!(optimalD; label="optimal GAN discriminator (scaled)") scene = plot(p1, size=(800,400), xlim=(-4, 4), ylim=(-0.3, 0.5), legend=:bottomright, legendfont=9)