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QuantEcon / Expectations.jl

Expectation operators for Distributions.jl objects
MIT License
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[feature request] The pareto case #68

Open lrnv opened 1 year ago

lrnv commented 1 year ago

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.

arnavs commented 1 year ago

Thanks @lrnv, this is great and actionable.

I'm sure the Pareto distribution would be super useful for economists. I'll have a look into it, or if you'd like to implement a PR, that would be great!