Installation (v1.0 and up):
pkg> add Expectations
This is a package designed to simplify the process of taking expectations of functions of random variables.
The underlying distributions are objects from Distributions.jl
(currently <:UnivariateDistribution
).
We support different types of Gaussian quadrature (Gauss-Hermite, Gauss-Legendre, Gauss-Laguerre, etc.) based on the distribution, as well as some methods with user-defined nodes (e.g., trapezoidal integration).
The key object is the expectation
function, which returns an operator:
dist = Normal()
E = expectation(dist)
E(x -> x)
For convenience, the operator can be applied directly to a function instead of being cached,
expectation(x->x^2, dist)
As a linear operator on vectors using the nodes of the distribution
dist = Normal()
E = expectation(dist)
x = nodes(E)
f(x) = x^2
E * f.(x) == dot(f.(x), weights(E))