Remove median(::MvLogNormal)

docs/src/multivariate.md

@@ -85,11 +85,10 @@ In addition to the methods listed in the common interface above, we also provide
 ```@docs
 location(::MvLogNormal)
 scale(::MvLogNormal)
-median(::MvLogNormal)
 mode(::MvLogNormal)
 ```
 
-It can be necessary to calculate the parameters of the lognormal (location vector and scale matrix) from a given covariance and mean, median or mode. To that end, the following functions are provided.
+It can be necessary to calculate the parameters of the lognormal (location vector and scale matrix) from a given covariance and mean or mode. To that end, the following functions are provided.
 
 ```@docs
 location{D<:Distributions.AbstractMvLogNormal}(::Type{D},s::Symbol,m::AbstractVector,S::AbstractMatrix)

src/multivariate/mvlognormal.jl

@@ -14,7 +14,6 @@
 #   - _logpdf(d,x)      Evaluate logarithm of pdf
 #   - _pdf(d,x)         Evaluate the pdf
 #   - mean(d)           Mean of the distribution
-#   - median(d)         Median of the distribution
 #   - mode(d)           Mode of the distribution
 #   - var(d)            Vector of element-wise variance
 #   - cov(d)            Covariance matrix
@@ -58,21 +57,14 @@ function _location!(::Type{D},::Type{Val{:mean}},mn::AbstractVector,S::AbstractM
     μ
 end
 
-function _location!(::Type{D},::Type{Val{:median}},md::AbstractVector,S::AbstractMatrix,μ::AbstractVector) where D<:AbstractMvLogNormal
-    @simd for i=1:length(md)
-      @inbounds μ[i] = log(md[i])
-    end
-    μ
-end
-
 function _location!(::Type{D},::Type{Val{:mode}},mo::AbstractVector,S::AbstractMatrix,μ::AbstractVector) where D<:AbstractMvLogNormal
     @simd for i=1:length(mo)
       @inbounds μ[i] = log(mo[i]) + S[i,i]
     end
     μ
 end
 
-###Functions to calculate location and scale for a distribution with desired :mean, :median or :mode and covariance
+###Functions to calculate location and scale for a distribution with desired :mean or :mode and covariance
 """
     location!{D<:AbstractMvLogNormal}(::Type{D},s::Symbol,m::AbstractVector,S::AbstractMatrix,μ::AbstractVector)
 
@@ -91,12 +83,11 @@ Calculate the location vector (the mean of the underlying normal distribution).
 
 - If `s == :meancov`, then m is taken as the mean, and S the covariance matrix of a
   lognormal distribution.
-- If `s == :mean | :median | :mode`, then m is taken as the mean, median or
+- If `s == :mean | :mode`, then m is taken as the mean or
   mode of the lognormal respectively, and S is interpreted as the scale matrix
   (the covariance of the underlying normal distribution).
 
-It is not possible to analytically calculate the location vector from e.g., median + covariance,
-or from mode + covariance.
+It is not possible to analytically calculate the location vector from e.g. from mode + covariance.
 """
 function location(::Type{D},s::Symbol,m::AbstractVector,S::AbstractMatrix) where D<:AbstractMvLogNormal
     @assert size(S) == (length(m),length(m))
@@ -209,17 +200,10 @@ scale(d::MvLogNormal) = cov(d.normal)
 #See https://en.wikipedia.org/wiki/Log-normal_distribution
 mean(d::MvLogNormal) = exp.(mean(d.normal) .+ var(d.normal)/2)
 
-"""
-    median(d::MvLogNormal)
-
-Return the median vector of the lognormal distribution. which is strictly smaller than the mean.
-"""
-median(d::MvLogNormal) = exp.(mean(d.normal))
-
 """
     mode(d::MvLogNormal)
 
-Return the mode vector of the lognormal distribution, which is strictly smaller than the mean and median.
+Return the mode vector of the lognormal distribution, which is strictly smaller than the mean.
 """
 mode(d::MvLogNormal) = exp.(mean(d.normal) .- var(d.normal))
 function cov(d::MvLogNormal)

test/multivariate/mvlognormal.jl

@@ -11,29 +11,21 @@ function test_mvlognormal(g::MvLogNormal, n_tsamples::Int=10^6,
                           rng::Union{AbstractRNG, Missing} = missing)
     d = length(g)
     mn = mean(g)
-    md = median(g)
     mo = mode(g)
     S = cov(g)
     s = var(g)
     e = entropy(g)
     @test partype(g) == Float64
     @test isa(mn, Vector{Float64})
-    if g.normal.μ isa Zeros{Float64,1}
-        @test md isa FillArrays.AbstractFill{Float64,1}
-    else
-        @test md isa Vector{Float64}
-    end
     @test isa(mo, Vector{Float64})
     @test isa(s, Vector{Float64})
     @test isa(S, Matrix{Float64})
     @test length(mn) == d
-    @test length(md) == d
     @test length(mo) == d
     @test length(s) == d
     @test size(S) == (d, d)
     @test s          ≈ diag(S)
     @test std(g)     ≈ sqrt.(diag(S)) 
-    @test md         ≈ exp.(mean(g.normal))
     @test mn         ≈ exp.(mean(g.normal) .+ var(g.normal)/2)
     @test mo         ≈ exp.(mean(g.normal) .- var(g.normal))
     @test entropy(g) ≈ d*(1 + Distributions.log2π)/2 + logdetcov(g.normal)/2 + sum(mean(g.normal))
@@ -51,15 +43,11 @@ function test_mvlognormal(g::MvLogNormal, n_tsamples::Int=10^6,
         X = rand(rng, g, n_tsamples)
     end
     emp_mn = vec(mean(X, dims=2))
-    emp_md = vec(median(X, dims=2))
     Z = X .- emp_mn
     emp_cov = (Z * Z') ./ n_tsamples
     for i = 1:d
         @test isapprox(emp_mn[i]   , mn[i] , atol=(sqrt(s[i] / n_tsamples) * 8.0))
     end
-    for i = 1:d
-        @test isapprox(emp_md[i]   , md[i] , atol=(sqrt(s[i] / n_tsamples) * 8.0))
-    end
     for i = 1:d, j = 1:d
         @test isapprox(emp_cov[i,j], S[i,j], atol=(sqrt(s[i] * s[j]) * 20.0) / sqrt(n_tsamples))
     end
@@ -77,13 +65,11 @@ function test_mvlognormal(g::MvLogNormal, n_tsamples::Int=10^6,
     # test the location and scale functions
     @test isapprox(location(g), location(MvLogNormal,:meancov,mean(g),cov(g))   , atol=1e-8)
     @test isapprox(location(g), location(MvLogNormal,:mean,mean(g),scale(g))    , atol=1e-8)
-    @test isapprox(location(g), location(MvLogNormal,:median,median(g),scale(g)), atol=1e-8)
     @test isapprox(location(g), location(MvLogNormal,:mode,mode(g),scale(g))    , atol=1e-8)
     @test isapprox(scale(g)   , scale(MvLogNormal,:meancov,mean(g),cov(g))      , atol=1e-8)
 
     @test isapprox(location(g), location!(MvLogNormal,:meancov,mean(g),cov(g),zero(mn))   , atol=1e-8)
     @test isapprox(location(g), location!(MvLogNormal,:mean,mean(g),scale(g),zero(mn))    , atol=1e-8)
-    @test isapprox(location(g), location!(MvLogNormal,:median,median(g),scale(g),zero(mn)), atol=1e-8)
     @test isapprox(location(g), location!(MvLogNormal,:mode,mode(g),scale(g),zero(mn))    , atol=1e-8)
     @test isapprox(scale(g)   , Distributions.scale!(MvLogNormal,:meancov,mean(g),cov(g),zero(S)), atol=1e-8)
 
@@ -100,7 +86,6 @@ end
     l1 = LogNormal(0.1, 0.4)
     l2 = MvLogNormal([0.1], 0.16 * I)
     @test [mean(l1)]     ≈ mean(l2)
-    @test [median(l1)]   ≈ median(l2)
     @test [mode(l1)]     ≈ mode(l2)
     @test [var(l1)]      ≈ var(l2)
     @test  entropy(l1)   ≈ entropy(l2)