Plotting the Gamma distribution sampling from it as a normalized histogram

gamma.jl

# Plotting the Gamma distribution and sample as a normalize histogram

using Distributions
using Gadfly

pdf(d::Gamma, x) = (x ^ (d.α - 1) * e ^ (-x / d.α)) / (d.θ ^ d.α * gamma(d.α))

n = 500

g = Gamma(2., 2.)

r = rand(g, n)

bins, counts = hist(r, 100)

# normalize on area of the histogram
counts_norm = counts / sum(counts * step(bins))

plot(
    layer(x=bins, y=[pdf(g, l + step(bins) / 2.) for l in bins], Geom.line, Theme(default_color=colorant"black")),
    layer(x=bins[1:end-1], y=counts_norm, Geom.bar),
)