This implements a numeric type, GVar, representing a Gaussian (normal) random variable. Some elementary mathematical functions of these variables are implemented, and these also return GVars giving the approximate distribution of the output.
Demo:
julia> using GaussianRandomVariables
julia> x = 5 ± 1
5.0 ± 1.0
julia> 1/x
0.20800000000000002 ± 0.041569219381653054
Related package: Measurements.jl is a much more fully-developed and featureful package which also handles arithmetic with Gaussian random variables. However, it implements first-order (linear) error propagation, which leads to different rules of arithmetic: compare
julia> using GaussianRandomVariables
julia> (0 ± 1)^2
1.0 ± 1.4142135623730951with
julia> using Measurements
julia> (0 ± 1)^2
0.0 ± 0.0Measurements is recommended for most users, but GaussianRandomVariables can be recommended if second-order accuracy matters in your application.
GaussianRandomVariables is built on top of ThickNumbers, and the API for working with GVars is described in detail there.