diff --git a/src/univariate/continuous/laplace.jl b/src/univariate/continuous/laplace.jl
index e853384e0..ebd3945ea 100644
--- a/src/univariate/continuous/laplace.jl
+++ b/src/univariate/continuous/laplace.jl
@@ -114,36 +114,10 @@ rand(rng::AbstractRNG, d::Laplace) =
 
 #### Fitting
 
-function fit_mle(::Type{<:Laplace}, x::AbstractArray{T}) where {T<:Real}
-    μ = median(x)
-    θ = zero(T)
-    for v ∈ x
-        θ += abs(v - μ)
-    end
-    θ /= length(x)
-    return Laplace(μ, θ)
-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)
+function fit_mle(::Type{<:Laplace}, x::AbstractArray{<:Real})
+    xc = similar(x)
+    copyto!(xc, x)
+    m = median!(xc)
+    xc .= abs.(x .- m)
+    return Laplace(m, mean(xc))
 end