compare_histograms.jl

"""
    freedman_diaconis(x)

Estimates the required bin width for the distribution x.

Freedman, D. and Diaconis, P., 1981. On the histogram as a density
estimator: L 2 theory. Zeitschrift für Wahrscheinlichkeitstheorie und
verwandte Gebiete, 57(4), pp.453-476.

"""
function freedman_diaconis(x)
   2 * iqr(x) / length(x)^(1/3)   
end

## colors not working well

function compare_histograms(dists; labels = nothing, colors= cgrad(:inferno), nbins = nothing)

    if labels == nothing
        labels = ["histogram $i" for i in 1:length(dists)]
    end
    
    p= plot()

    mmin = floor(minimum([minimum(x) for x in dists]))
    mmax = ceil(maximum([maximum(x) for x in dists])) + 1

    if nbins == nothing
        h = minimum([freedman_diaconis(x) for x in dists])
        nbins = (mmax - mmin) / h
    else
        h = (mmax - mmin) / nbins
    end
    

    println("step $h")
    println("nbins $nbins")
      
    for i in 1:length(dists)
        a = fit(Histogram, dists[i], mmin:h:mmax, closed=:left)
        plot!(a.edges[1][1:end-1], a.weights,  color=colors[i],label=labels[i])

    end

    return p
end