Comparing two ways of computing expectations in Julia

gistfile1.jl

using Distributions
using Calculus
using Benchmark

function expectation(distr::Distribution,
                   g::Function,
	                 epsilon::Real)
    f = x -> pdf(distr, x)
    endpoints = map(e -> quantile(distr, e), (epsilon, 1 - epsilon))
    integrate(x -> f(x) * g(x), endpoints[1], endpoints[2])
end

function expectation2(distr::Distribution,
	                  g::Function,
	                  epsilon::Real)
    f(x::Real) = pdf(distr, x)
    endpoints = map(e -> quantile(distr, e), (epsilon, 1 - epsilon))
    h(x::Real) = f(x) * g(x)
    integrate(h, endpoints[1], endpoints[2])
end

e1() = expectation(Normal(0, 1), identity, 1e-5)
e2() = expectation2(Normal(0, 1), identity, 1e-5)

compare([e1, e2], 10000)