dummy-link

0

0

0

1

# SimpleProbabilitySets.jl

A collection of ambiguity sets, or sets of probability distributions.

## Installation

This application is built for Julia 0.6. If not already installed, the application can be cloned using

``````Pkg.clone("https://github.com/ajkeith/SimpleProbabilitySets.jl")
``````

## Usage

`SimpleProbabilitySets.jl` currently includes discrete P-boxes and discrete interval probability sets.

Discrete interval-based probability sets contain all probability distributions such that the probability of each component belongs to a pre-defined interval. The intervals can be defined componentwise. Note that `plower` and `pupper` are a set of lower and upper interval bounds, not probability distributions.

``````using SimpleProbabilitySets

plower = [0.1, 0.2, 0.5]
pupper = [0.4, 0.4, 0.7]
pset1 = PInterval(plower, pupper)
``````

The discrete interval-based probability set can also be defined using a nominal distribution and an interval half-width.

``````using SimpleProbabilitySets

dnominal = [0.1, 0.2, 0.5]
halfwidth = 0.05
pset2 = PInterval(dnominal, halfwidth)
``````

Use the Distributions.jl package to build a P-box from an upper and lower distribution. A discrete P-box containts all probability ditrubtions whose CDF belongs to a set of CDFs defined by an "upper" and "lower" CDF.

``````using SimpleProbabilitySets
using Distributions

dlower = Categorical([0.1, 0.2, 0.7])
dupper = Categorical([0.4, 0.4, 0.2])
pset3 = PBox(dlower, dupper)
``````

## Sampling

To sample a probabiliy distribution from the set of distributions, use

``````psample(plower, pupper)
``````

where `plower` and `pupper` are vectors of lower and upper interval bounds. This sampling function calls the R library `hitandrun` with details published in Tervonen et al. (2013).

## References

If this code is useful to you, please star this package and consider citing the following paper.

Tervonen, T., van Valkenhoef, G., Baştürk, N., & Postmus, D. (2013). Hit-And-Run enables efficient weight generation for simulation-based multiple criteria decision analysis. European Journal of Operational Research, 224(3), 552–559. https://doi.org/10.1016/j.ejor.2012.08.026

09/12/2018

over 2 years ago

9 commits