Plotting mixtures of distributions with Julia

Question

I want to plotting mixtures of two 1d Gaussian distributions with Julia. I am not sure what is the best way to do it. I am trying to use Distributions.jl and in specific to both

• Define two Gaussians using d1 = Normal(0.0, 1.0) and d2 = Normal(1.0, 1.8)
• Define a mixture using MixtureModel(Normal[ Normal(-2.0, 1.2), Normal(0.0, 1.0), Normal(3.0, 2.5)], [0.1, 0.6, 0.3])

Now, for the 1st attempt I do not know how to define the weights. My questions therefore is about how to proceed on to simply generate and draw samples of this mixture?

I would like to plot them and also use these samples in order to perform parameter estimation.

Answer 1

I'm not sure I fully understand the question - why are you defining d1 and d2?

To answer your bold question: just use rand() to draw from your mixture distribution:

julia> using Distributions

julia> mm = MixtureModel([Normal(-2.0, 1.2), Normal(), Normal(3.0, 2.5)], [0.1, 0.6, 0.3])
MixtureModel{Normal{Float64}}(K = 3)
components[1] (prior = 0.1000): Normal{Float64}(μ=-2.0, σ=1.2)
components[2] (prior = 0.6000): Normal{Float64}(μ=0.0, σ=1.0)
components[3] (prior = 0.3000): Normal{Float64}(μ=3.0, σ=2.5)

julia> rand(mm)
1.882130062980293

Note that here I have used Normal() instead of Normal(0.0, 1.0), as Normal() already returns the standard normal distribution.

To plot:

julia> using Plots

julia> histogram(rand(mm, 100_000), normalize = true, xlabel = "Value", ylabel = "Frequency", label = "Mixture model")