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Implement Dirac distribution #861
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,30 @@ | ||
| """ | ||
| Dirac(value) | ||
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| A *Dirac distribution* is parametrized by its only value, and takes its value with probability 1. | ||
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| ```julia | ||
| d = Dirac(2.0) # Dirac distribution with value = 2. | ||
| rand(d) # Always returns the same value | ||
| ``` | ||
| """ | ||
| struct Dirac{T} <: DiscreteUnivariateDistribution | ||
| value::T | ||
| end | ||
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| eltype(::Dirac{T}) where {T} = T | ||
| rand(rng::AbstractRNG, d::Dirac) = d.value | ||
| pdf(d::Dirac, x::Real) = x == d.value ? 1.0 : 0.0 | ||
| cdf(d::Dirac, x::Real) = x < d.value ? 0.0 : 1.0 | ||
| quantile(d::Dirac{T}, p) where {T} = 0 <= p <= 1 ? d.value : T(NaN) | ||
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| minimum(d::Dirac) = d.value | ||
| maximum(d::Dirac) = d.value | ||
| insupport(d::Dirac, x) = x == d.value | ||
| mean(d::Dirac) = d.value | ||
| var(d::Dirac) = 0.0 | ||
| mode(d::Dirac) = d.value | ||
| skewness(d::Dirac) = 0.0 | ||
| kurtosis(d::Dirac) = 0.0 | ||
| entropy(d::Dirac) = 0.0 | ||
| mgf(d::Dirac, t) = exp(t * d.value) | ||
| cf(d::Dirac, t) = exp(im * t * d.value) | ||
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,20 @@ | ||
| using Distributions | ||
| using Test | ||
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| @testset "Dirac tests" begin | ||
| for val in [3, 3.0] | ||
| d = Dirac(val) | ||
| @test minimum(d) == val | ||
| @test maximum(d) == val | ||
| @test pdf(d, val - 1) == 0 | ||
| @test pdf(d, val) == 1 | ||
| @test pdf(d, val + 1) == 0 | ||
| @test cdf(d, val - 1) == 0 | ||
| @test cdf(d, val) == 1 | ||
| @test cdf(d, val + 1) == 1 | ||
| @test quantile(d, 0) == val | ||
| @test quantile(d, 0.5) == val | ||
| @test quantile(d, 1) == val | ||
| @test rand(d) == val | ||
| end | ||
| end |
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Dirac Delta is a Continuous distribution
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No, it doesn't have a density with respect to the Lebesgue measure, so it is not a "continuous probability distribution" (not to mix with distributions in Schwartz' sense.)
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According to the documentation
ValueSupportcan take valuesDiscrete(Samples take discreteIntvalues) andContinuous(samples take continuous realFloat64values). So in this sense, it seems that the Dirac delta should beContinuous. I think that your interpretation would leave many useful measures completely out of the hierarchy (e.g. mixtures of continuous and discrete such as Spike-and-Slab)There was a problem hiding this comment.
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That is, according to the documentation the trait "Continuous" seems to refer only to the set on which the distribution is defined (the real line), not to the fact that it is absolutely continuous with respect to the Lebesgue measure.