# Questions tagged [laplace-distribution]

Use this tag when asking questions about the Laplace distribution. This probability distribution is sometimes called the double exponential distribution (not to be confused with the Gumbel distribution).

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### Expected absolute deviation greater than standard Laplace

Could there exist a distribution, other than standard Laplace (probability density of the form $1/2e^{-|x|}$), on $\mathbb{R}$ such that $E[x]=0,E[|x|]=1$ and that \begin{equation*} E[|x-a|] \geq |a|+...
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### Posterior computation for Laplace distribution

I am dealing with being Bayesian and looking for a closed form for a posterior for the scale parameter $\tau$ of a Laplace distribution, such that I can derive a full conditional in my Gibbs sampler. ...
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### Standard Error of the MLE for Laplace Distribution

Given the Laplace distribution parametrized by $\mu$ and $b$, $f(x\mid \mu ,b)={\frac {1}{2b}}\exp \left(-{\frac {|x-\mu |}{b}}\right)\,\!$ , I know that $\hat \mu$, the maximum likelihood ...
Say we have $f(x , \theta) = \frac{1}{2}e^{-|x-\theta|}$ Lets assume for simplicity, we only have 1 sample. We find that the log-likelihood for this distribution is:  l(\theta , x) = -log(2) + (\...