CustomSampler https://pasteboard.co/IBirbG7.gif

HW2.jl

using Plots, Statistics
using StatsPlots
using Distributions #this pkg actually is end game, but we're just using gaussian pdf

function custom_gaussian(n)
    #b)
    #parent distribution is Gaussian
    μ = 10
    parent = Distributions.Normal(10) #μ = 10
    parent_pdf(x) = Distributions.pdf(parent, x)

    #c)
    rᵢ = rand(n)

    #d)
    a = 6
    b = 14
    xᵢ = a .+ (b-a) .* rᵢ

    #e)
    βᵢ = parent_pdf.(xᵢ) ./ parent_pdf(median(xᵢ))

    #f)
    sᵢ = rand(n)
    msk = βᵢ .> sᵢ
    result = xᵢ[msk]
end

big_array = []
@gif for n = 1:11^2
    append!(big_array, custom_gaussian(25))
    histogram(big_array, bin=7:0.3:13, normed=true, label="Normalized hist")
    plot!(Normal(10), label="True PDF")
    title!("Customized sampler with n=$(n*1000)")
end

https://pasteboard.co/IBirbG7.gif