Laplace (Double Exponential, Bilateral Exponential) Distribution

The ML estimator of the location parameter is

where $X_i$ is a sequence of $N$ mutually independent Laplace RV's and the median is some number between the $\frac{1}{2}N\mathrm{th}$ and the $(N/2+1)\mathrm{th}$ order statistic ( e.g. take the average of these two) when $N$ is even. Also,

Replace $\hat{L}$ with $L$ if it is known. If $L$ is known then this estimator is distributed as ${\left(2N\right)}^{-1}S\cdot {\chi }_{2N}^2$ .

Implementation: scipy.stats.laplace