Constructing probability boxes
A probability distribution can be created by using it's shape and parameters:
julia> a = normal(0,1)
Pbox: ~ normal ( range=[-3.090232,3.090232], mean=0.0, var=1.0)In ProbabilityBoundsAnalysis.jl probability distributions are p-boxes, but with equal bounds and precise moments.
The IntervalArithmetic.jl package is used to create intervals:
julia> b = interval(0,1)
[0, 1]IntervalArithmetic.jl will work natively with ProbabilityBoundsAnalysis.jl, however an interval can be converted to a p-box in the following way:
julia> b = makepbox(interval(0,1))
Pbox: ~ ( range=[0.0,1.0], mean=[0.0,1.0], var=[0.0,0.25])There are a number of ways that p-boxes can be created. For example they are the result of arithemtic between random variables with unknown dependence. They can also be defined by using a distributions shape but with interval parameters:
julia> c = normal(interval(0,1),1)
Pbox: ~ normal ( range=[-3.09023,4.0902322], mean=[0.0,1.0], var=1.0)or by taking the envelope over a number of uncertain numbers:
julia> d = normal(-1,1);
julia> e = normal(1, interval(1,2));
julia> f = env(d,e)
Pbox: ~ normal ( range=[-5.18046,7.1804646], mean=[-1.0,1.0], var=[1.0,4.0])and may be plotted as follows:
julia> using PyPlot
julia> plot(f)
In ProbabilityBoundsAnalysis.jl all plots of uncertain numbers are of their cdfs.
Supported parametric distributions:
- normal
- uniform
- beta
- betaPrime
- biweght
- cauchy
- chi
- chisq
- cosine
- epanechnikov
- erlang
- exponential
Supported distribution free p-boxes:
- meanVar
- meanMin
- meanMax
- meanMinMax
- minMaxMeanVar
KN c-boxes also supported.
All constructors support interval arguments.