QuantEcon / QuantEcon/Expectations.jl
[feature request] The pareto case
Nobody has claimed this yet.
- Dominant language
- Julia
- Stars
- 61
- Forks
- 15
- PR merge metrics
- No merged PRs in 30d
Description
The Pareto case could be handled by using the fact that if $X$ is Pareto-dsitributed with minimal value $m$ and shape index $\alpha$, then
$$Y = log(X) - log(m)$$ is exponentially distributed with rate parameter $\alpha$. Therefore, for any function $f$,
$$\mathbb E(f(X)) = \mathbb E(f(m * e^Y))$$
and we can re-use the quadrature scheme of $Y$, which follows a Exponential(\alpha) distribution.
Contributor guide
No contributing guide indexed for this repository
First steps
- Read the whole issue, then the project's contributing guide.
- Comment on the issue to say you are picking it up — it saves two people doing the same work.
- Fork the repository and make your change on a branch.
- Open a pull request that references the issue number.
Research direction
Start by locating the quadrature implementation for exponential distributions and the existing distribution-specific tests. Implement the Pareto case using the logarithmic transformation described in the issue, then verify that expectations for Pareto-distributed inputs match the transformed exponential calculation.
Written by the indexing model from the issue text.
Assessment
- Tech stack
- julia
- Domain
- data
- Issue type
- Feature
- Difficulty
- 3/5
- Estimated time
- 1-2 days
- Activity status
- Stale
- Clarity
- Mostly clear
- Newbie friendliness
- 42/100