Distributions

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

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.

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