Distributions
Marchenko-Pastur
RandomMatrix.MarchenkoPastur
— TypeMarchenkoPastur <:ContinuousUnivariateDistribution
MarchenkoPastur(λ,σ)
pdf(d::MarchenkoPastur,x::Real)
λ
: default0.5
σ
: default1
Examples
Generate a MP rv with ρ = 0.5, σ = 1
rand(MarchenkoPastur())
1.2656480923753979
Compute the desity for the MP distribution with λ=1.6 at the point 0
pdf(MarchenkoPastur(1.6),0)
0.375
Generate 100 MP rvs with ρ=0.1 and σ = 2
rand(MarchenkoPastur(0.1,2),100)
100-element Vector{Float64}:
5.31001367107032
2.3707745658317116
2.5378523986772343
2.585256212138476
⋮
3.66799182506567
6.517865226831382
3.7628212250212423
4.582520400697299
Circular Law
RandomMatrix.Circular
— TypeCircular(c=0,R=1)
- The uniform distribution on the complex disk with center
c
and radiusR
rand(Circular(1,10),200)
Generates 200 uniform r.v.s on the complex disk of center 1 radius 10.
Elliptic Law
RandomMatrix.Elliptic
— TypeElliptic <:ContinuousUnivariateDistribution
Elliptic(ρ;c,R)
- the uniform rv on an ellipse of width
2(1+ρ)R
, height2(1-ρ)R
centered atc