Distributions

All distributions provided in this package are organized in a type hierarchy as follows:

abstract Distribution
distribution <: Distribution

Here is the list of implemented distribution. This list will grow as I continue to develop this package.

• Gaussian1D
• Dirichlet

Gaussian1D

Gaussian1D is the univariate Gaussian distribution. It is parametrized by its mean and variance.

julia> using BIAS
julia> srand(123)

julia> qq = Gaussian1D(5, 2)
Gaussian1D distribution
mean: mu=5.0, variance: vv=2.0

julia> sample(qq)
6.683292

julia> sample(qq, 100)
100-element Array{Float64, 1}:
7.89656
6.61595
...

julia> pdf(qq, 4.5)
0.265003

julia> logpdf(qq, 4.5)
-1.328012

Dirichlet

Dirichlet distribution is a probability distribution on a probability simplex where its draws are multinomial random variables.

julia> qq = Dirichlet([0.2, 0.2, 0.2, 0.2])
Dirichlet distribution
cardinality = 4
alpha       = [0.2,0.2,0.2,0.2]

julia> qq = Dirichlet(5, 4)
Dirichlet distribution
cardinality = 4
alpha       = [1.25,1.25,1.25,1.25]

julia> mean(qq)
4-elemnt Array{Float64, 1}
0.25
0.25
0.25
0.25

Caution

pdf and logpdf need to be revised.