Installation (for Julia 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 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,
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))
The underlying distributions are objects from
Starting with 1.3.0, we also support mixture models.
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).
We have rules for the following distributions:
- Continuous Univariate (compact; generic fallback)
- Continuous Univariate (no restriction; approximates with quantile grid)
See docs for more info.
We also support mixture models, e.g.
d = MixtureModel([Uniform(), Normal(), Gamma()]); E = expectation(d); E(x -> x) # 0.5000000000000016
MixtureExpectation objects support most of the same behavior as the individual
2E(x -> x) # 1.000000000000003 weights(E) # [1/3, 1/3, 1/3] expectations(E) # component expectations