Improvements to plotting PMFs for discrete distributions

[sethaxen]

This PR fixes #450 and fixes #287.

[devmotion]

I think it would be easier (and probably faster) to not use detault_range but

• to look up min_dist, max_dist = extrema(dist) (that will always work)
• to use support if both are bounded (this should also work, the bug in Distributions only affects unbounded support)
• and to use the quantiles with a unit range in the other case (which is likely wrong in some cases but probably the best one can do right now)

[devmotion]

I guess it's the best that can be done currently. Maybe it would be a good opportunity to address #287 as well.

[sethaxen]

Maybe it would be a good opportunity to address #287 as well.

Done!

julia> plot(Binomial(50, 0.5))

[sethaxen]

I made the same work for discrete mixtures. e.g. here is zero-inflated Poisson:

julia> zip = MixtureModel([Dirac(0), Poisson(10)], [0.1, 0.9])
MixtureModel{Distribution{Univariate, Discrete}}(K = 2)
components[1] (prior = 0.1000): Dirac{Int64}(value=0)
components[2] (prior = 0.9000): Poisson{Float64}(λ=10.0)

julia> plot(zip)

julia> plot(zip; components=false)

[daschw]

Nice, thanks a lot!

[devmotion]

I wonder if one has to include markers for :sticks by default?

[devmotion]

I guess this is more likely to be type unstable than the current implementation?

[sethaxen]

Why? It turns out this is necessary for the zero-inflated Poisson to not make everything a Float64. Since logpdf for discrete MixtureModel only accepts points of type Int, this turning everything into floats causes failures.

[devmotion]

Because in the loop the type of minval and maxval will be changed for most distributions: for most distributions minimum, maximum and quantile do not return values of type Int. It's also not guaranteed that they are of type Float64 but this is definitely more likely for continuous distributions (and it would still be type stable for distributions where these values are of type Int if one uses min and max to update minval and maxval in the loop).

logpdf and pdf accept Real regardless if the distribution is discrete or not. If there's a problem with MixtureModel, it has to be fixed in Distributions.

[sethaxen]

Because in the loop the type of minval and maxval will be changed for most distributions: for most distributions minimum, maximum and quantile do not return values of type Int. It's also not guaranteed that they are of type Float64 but this is definitely more likely for continuous distributions (and it would still be type stable for distributions where these values are of type Int if one uses min and max to update minval and maxval in the loop).

We should support both though, not just continuous distributions. I pushed an implementation using mapreduce that is simpler and does this.

[sethaxen]

I wonder if one has to include markers for :sticks by default?

Can you clarify what you mean?

[devmotion]

If it is necessary to set markershape or if one should just not plot markers with the default settings.

[sethaxen]

If it is necessary to set markershape or if one should just not plot markers with the default settings.

Setting markershape is necessary to show the markers as suggested in the original issue. Personally, I prefer hair plots without markers and would prefer the simplicity of not explicitly showing them and letting the user do it if they want it. What do you think?

[devmotion]

Personally, I prefer hair plots without markers and would prefer the simplicity of not explicitly showing them and letting the user do it if they want it.

Yes, my question was if you think it would be preferrable to not show them explicitly. I prefer the version without markers (IMO it is a bit cleaner, in particular if there are many values to plot) and it seems simple enough to specify markershape if one wants to plot points as well.

[sethaxen]

Okay, I simplified the implementation to not show markers by default.

julia> plot(Binomial(50, 0.5))

For plots with few points, in my view this looks worse:

julia> plot(plot(Binomial(5, 0.1)), plot(Binomial(5, 0.1); markershape=:circle))

But it looks much better for plots with many points:

julia> plot(plot(Poisson(500)), plot(Poisson(500); markershape=:circle); legend=:left)