https://github.com/QuantEcon/Expectations.jl

Expectation operators for Distributions.jl objects
https://github.com/QuantEcon/Expectations.jl

distributions julia quadrature statistics

Last synced: about 2 months ago
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Expectation operators for Distributions.jl objects

• Host: GitHub
• URL: https://github.com/QuantEcon/Expectations.jl
• Owner: QuantEcon
• License: mit
• Created: 2018-07-10T17:11:18.000Z (about 6 years ago)
• Default Branch: master
• Last Pushed: 2024-01-02T20:49:04.000Z (9 months ago)
• Last Synced: 2024-05-22T17:17:42.448Z (4 months ago)
• Topics: distributions, julia, quadrature, statistics
• Language: Julia
• Homepage:
• Size: 266 KB
• Stars: 56
• Watchers: 6
• Forks: 15
• Open Issues: 7
• Metadata Files:
  • Readme: README.md
  • License: LICENSE.md

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README

        
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# Expectations

Installation (for Julia v1.0 and up):

```julia

pkg> add Expectations

```

See [Pkg docs for more details](https://julialang.github.io/Pkg.jl/v1/managing-packages/#Adding-packages-1)

This is a package designed to simplify the process of taking expectations of functions of random variables.

### Expectation Operator

The key object is the `expectation` function, which returns an operator:

```julia

dist = Normal()

E = expectation(dist)

E(x -> x)

```

For convenience, the operator can be applied directly to a function instead of being cached,

```julia

expectation(x->x^2, dist)

```

As a linear operator on vectors using the nodes of the distribution

```julia

dist = Normal()

E = expectation(dist)

x = nodes(E)

f(x) = x^2

E * f.(x) == dot(f.(x), weights(E))

```

### Random Variables

The underlying distributions are objects from `Distributions.jl` (currently `<:UnivariateDistribution`).

**Starting with 1.3.0, we also support mixture models.**

### Quadrature Algorithms

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:

* Normal

* ChiSq

* LogNormal

* Exponential

* Beta

* Gamma/Erlang

* Uniform

* Continuous Univariate (compact; generic fallback)

* Continuous Univariate (no restriction; approximates with quantile grid)

* Discrete

See docs for more info.

### Mixture Models

We also support mixture models, e.g.

```julia

d = MixtureModel([Uniform(), Normal(), Gamma()]);

E = expectation(d);

E(x -> x) # 0.5000000000000016

```

The `MixtureExpectation` objects support most of the same behavior as the individual `IterableExpectation`s.

```julia

2E(x -> x) # 1.000000000000003

weights(E) # [1/3, 1/3, 1/3]

expectations(E) # component expectations

```