The Dist object contains information for convolving random variables.

• lb: lower bound of density
• ub: upper bound of density
• n_points: number of discrete points used in transform
• x: real values associated with densities
• density: densities resulting from Convolution
• interp_pdf: an object used to interpolate exact densities from x and density

model = Normal(0,1) + Normal(0,1)
convolve!(model)

julia> pdf(model, 0.0)
0.28216441829987216

julia> pdf(Normal(0,sqrt(2)), 0.0)
0.28209479177387814

cf is a closed form approximation for the Lognormal characteristic function. See the following for details: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.720.1797&rep=rep1&type=pdf

Convolves a set of random variables.

model = Normal(0,1) + Normal(0,1)
convolve!(model)

julia> pdf(model, 0.0)
0.28216441829987216

julia> pdf(Normal(0,sqrt(2)), 0.0)
0.28209479177387814

Normal approximation to the sum of Uniform rvs

• 'scaling' = (2/3): default scaling used for standard deviation σ
• 'args': a list of NamedTuples for component distributions, e.g. cr =(μ=.05,N=2),...

julia> μ,σ = convolve_normal(cr=(μ=.05,N=2),vis=(μ=.085,N=1))
(0.185, 0.021278575558006173)