Talk:Log-Laplace distribution

This article is rated Stub-class on Wikipedia's content assessment scale. It is of interest to the following WikiProjects:

Statistics Low‑importance This article is within the scope of WikiProject Statistics, a collaborative effort to improve the coverage of statistics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.StatisticsWikipedia:WikiProject StatisticsTemplate:WikiProject StatisticsStatistics articles Low This article has been rated as Low-importance on the importance scale.

If $Y\sim\mathrm{Lap}(b)$ has a Laplace distribution

$$ p(y) = \frac{1}{2b} \exp\left(- \frac{\abs{x}}{b}\right)$$

Then $X = \exp(Y)$ has a Log-Laplace distribution with pdf

$$ p(x) = \frac{1}{2b}

\begin{cases}

x^{b^{-1}-1} &\text{ for } 0 < x < 1 \\

x^{-b^{-1}-1} &\text{ for } x \geq 1

\end{cases}

$$

This would then also match the plots! One could also add that this is closely related to a certain Pareto distribution (e.g. when b=1) The current version forgets that |log(x)| is not equal to log(x) for 0<x<1

169.234.245.100 (talk) 03:08, 25 April 2024 (UTC)[reply]