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Dirac: Implement location, scale, affine transformation #1735

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Dirac: Implement location, scale, affine transformation #1735

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Dirac: Implement location, scale, affine transformation
i9e1 Jun 6, 2023
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i9e1 Jul 2, 2023
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10 changes: 9 additions & 1 deletion src/univariate/discrete/dirac.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -18,7 +18,7 @@ External links:

* [Dirac measure on Wikipedia](http://en.wikipedia.org/wiki/Dirac_measure)
"""
struct Dirac{T} <: DiscreteUnivariateDistribution
struct Dirac{T<:Real} <: DiscreteUnivariateDistribution
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value::T
end

Expand All @@ -29,6 +29,9 @@ minimum(d::Dirac) = d.value
maximum(d::Dirac) = d.value
support(d::Dirac) = (d.value,)

location(d::Dirac) = d.value
scale(d::Dirac{T}) where {T} = one(T)
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#### Properties
mean(d::Dirac) = d.value
var(d::Dirac{T}) where {T} = zero(T)
Expand All @@ -53,6 +56,11 @@ mgf(d::Dirac, t) = exp(t * d.value)
cgf(d::Dirac, t) = t*d.value
cf(d::Dirac, t) = cis(t * d.value)

#### Affine transformation
Base.:+(d::Dirac, c::Real) = Dirac(d.value + c)
Base.:+(a::Dirac, b::Dirac) = Dirac(a.value + b.value)
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Base.:*(c::Real, d::Dirac) = Dirac(c * d.value)

#### Sampling

rand(rng::AbstractRNG, d::Dirac) = d.value
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