Make TracyWidom order a type parameter?

[dahong67]

Hi! Thanks all for this nice package, I'm quite happily using it to evaluate the Tracy-Widom law of order 1. :)

I was wondering if it might make sense to make TracyWidom a parametric type with the order/index beta as the parameter, i.e., replace

struct TracyWidom <: ContinuousUnivariateDistribution end

with

struct TracyWidom{β} <: ContinuousUnivariateDistribution end

This seems conceptually nice, and (as far as I could tell) would also simplify some of the code by replacing if/else statements in the current code with dispatch (e.g., https://github.com/JuliaMath/RandomMatrices.jl/blob/master/src/densities/TracyWidom.jl#L63-L77).

If interested, I'd be happy to try it out in a pull request!

[dlfivefifty]

Why in the type? Alternatively we can do

struct TracyWidom{T} <: ContinuousUnivariateDistribution
    β::T
end

A good reason to prefer this is to support BigFloat.

[dlfivefifty]

If interested, I'd be happy to try it out in a pull request!

Yes please!

[dahong67]

Great! I'll get started on one. :)

Making β a field rather than type parameter is an interesting idea, and supporting BigFloat is a neat point! On a related note, I'm (personally) only familiar with Tracy-Widom for β = 1,2,4. Do you have a reference you'd recommend for other β's being used?

One advantage of putting β in the type is that we could then dispatch on it.

[dlfivefifty]

Dumitriu and Edelman have a lot of papers on general β. The easiest construction is via a tridiagonal matrix with χ distributed off diagonal entries

I can’t see why one would need dispatch, an if statement will be just as convenient

[dahong67]

Ah right, thanks so much for the pointer! I also thought some more and agree with you that there is not really a need for dispatch here.

I'll start the pull request once I get some free time - hopefully this weekend!