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Weighted MLE fit for Laplace distribution with unit test #1310

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Weighted MLE fit for Laplace distribution with unit test #1310

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520e154
added weighted fit for Laplace distribution
salbert83 Apr 21, 2021
6b1da51
effiency improvements
salbert83 Apr 21, 2021
059a237
bug fix
salbert83 Apr 21, 2021
857debf
improvements suggested by David Widmann
salbert83 Apr 21, 2021
76f9cc2
Merge branch 'master' of https://github.com/salbert83/Distributions.jl
salbert83 Apr 22, 2021
3820926
MLE fit for weighted Laplace with unit test
salbert83 Apr 22, 2021
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24 changes: 24 additions & 0 deletions src/univariate/continuous/laplace.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -121,3 +121,27 @@ function fit_mle(::Type{<:Laplace}, x::AbstractArray{<:Real})
xc .= abs.(x .- m)
return Laplace(m, mean(xc))
end

function fit_mle(::Type{<:Laplace}, x::AbstractArray{T}, w::AbstractArray{T}) where {T <: Real}
sp = sortperm(x)
n = length(x)
sw = sum(w)
highsum = sw
lowsum = zero(T)
idx = 0
for i = 1:n
lowsum += w[sp[i]]
highsum -= w[sp[i]]
if lowsum >= highsum
idx = sp[i]
break
end
end
μ = x[idx]
θ = zero(T)
for i = 1:length(x)
θ += w[i] * abs(x[i] - μ)
end
θ /= sw
return Laplace(μ, θ)
Comment on lines +125 to +146
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I would suggest to use AbstractWeights (from StatsBase) since this allows to use different types of weights and existing optimized algorithms. E.g., one should then probably just use median(x, weights) defined in StatsBase and mean(abs.(x .- m), weights) (also defined in StatsBase). This creates more memory allocations than in the unweighted case but I think it is fine since the code complexity (and hence the risk of introducing bugs) is much lower.

end
9 changes: 9 additions & 0 deletions test/fit.jl
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Expand Up @@ -362,6 +362,15 @@ end
end
end

@testset "Testing fit for Laplace with weights" begin
for func in funcs, dist in (Laplace, Laplace{Float64})
d = fit(dist, func[2](dist(5.0, 3.0), N + 1), ones(Float64, N+1))
@test isa(d, dist)
@test isapprox(location(d), 5.0, atol=0.01)
@test isapprox(scale(d) , 3.0, atol=0.01)
end
end

@testset "Testing fit for Pareto" begin
for func in funcs, dist in (Pareto, Pareto{Float64})
x = func[2](dist(3., 7.), N)
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