fix fit for Laplace distribution (#1309)

Co-authored-by: David Widmann <dev+github@devmotion.de>

Project.toml

@@ -1,7 +1,7 @@
 name = "Distributions"
 uuid = "31c24e10-a181-5473-b8eb-7969acd0382f"
 authors = ["JuliaStats"]
-version = "0.24.17"
+version = "0.24.18"
 
 [deps]
 FillArrays = "1a297f60-69ca-5386-bcde-b61e274b549b"

src/univariate/continuous/laplace.jl

@@ -114,8 +114,10 @@ rand(rng::AbstractRNG, d::Laplace) =
 
 #### Fitting
 
-function fit_mle(::Type{<:Laplace}, x::Array)
-    xc = copy(x)
-    a = median!(xc)
-    Laplace(a, StatsBase.mad!(xc, center=a))
+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

test/fit.jl

@@ -355,10 +355,10 @@ end
 
 @testset "Testing fit for Laplace" begin
     for func in funcs, dist in (Laplace, Laplace{Float64})
-        d = fit(dist, func[2](dist(5.0, 3.0), N))
+        d = fit(dist, func[2](dist(5.0, 3.0), N + 1))
         @test isa(d, dist)
-        @test isapprox(location(d), 5.0, atol=0.1)
-        @test isapprox(scale(d)   , 3.0, atol=0.2)
+        @test isapprox(location(d), 5.0, atol=0.02)
+        @test isapprox(scale(d)   , 3.0, atol=0.02)
     end
 end