In the original code the parameters are called xi and x0. Here is a quick overview how they shape the distribution:
using PGFPlotsX
using LaTeXStrings
using Colors
push!(PGFPlotsX.CUSTOM_PREAMBLE, raw"\pgfplotsset{scale=2.0}")
xs = range(-10, 40; length=500)
@pgf axis = Axis({no_marks, ultra_thick})
xis = 1:2:10
x0s = 1:2:10
for (xi, color) ∈ zip(xis, distinguishable_colors(length(xis), [RGB(1,0,0), RGB(0,0,0)]))
for (x0, alpha) ∈ zip(x0s, range(1, 0.2; length=length(x0s)))
push!(axis, @pgf Plot({color = color, opacity = alpha}, Coordinates(xs, [landau_pdf(x, xi, x0) for x ∈ xs])))
push!(axis, LegendEntry("xi = $xi, x0 = $x0"))
end
end
axis
