# Distributions

## Marchenko-Pastur

RandomMatrix.MarchenkoPasturType
MarchenkoPastur <:ContinuousUnivariateDistribution

MarchenkoPastur(λ,σ)
pdf(d::MarchenkoPastur,x::Real)  
• λ : default 0.5
• σ : default 1

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
source

## Circular Law

RandomMatrix.CircularType
Circular(c=0,R=1)
• The uniform distribution on the complex disk with center c and radius R
rand(Circular(1,10),200)

Generates 200 uniform r.v.s on the complex disk of center 1 radius 10.

source

## Elliptic Law

RandomMatrix.EllipticType
Elliptic <:ContinuousUnivariateDistribution

Elliptic(ρ;c,R)
• the uniform rv on an ellipse of width 2(1+ρ)R, height 2(1-ρ)R centered at c
source