Talk:Log-Laplace distribution

pdf is clearly wrong!
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)