Feature request: deterministic (Dirac) distribution

[HenriDeh]

Following this discussion, it appears the package could use a distribution that returns a fixed value.

In physics it is called a Dirac. It would be defined as

struct Dirac{T<:Real} <: ContinuousUnivariateDistribution
    x::T
end

function rand(dist::Dirac)
    return dist.x
end

dist = Dirac(1.0)
rand(dist) #returns 1.0

We should also add a multivariate equivalent where T<:Array{<:Real}

[johnczito]

A Normal with zero variance behaves this way

julia> d = Normal(4.5, 0.0)
Normal{Float64}(μ=4.5, σ=0.0)

julia> rand(d)
4.5

julia> logpdf(d, 4.5)
Inf

julia> logpdf(d, 5.0)
-Inf

So one approach is just to say

Dirac(x::Real) = Normal(x, zero(x))

[HenriDeh]

Is it still interesting to define a Dirac struct in the repo ? One would only add the definition you propose and it would suffice

[nickrobinson251]

There's an open PR, and I'm sure help getting it over the line would be appreciated :) https://github.com/JuliaStats/Distributions.jl/pull/861/files

[devmotion]

Fixed by #1231.