# 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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### OLS vs MLE when errors are not normally distributed (Laplace distributed)

We say that under assumptions of the Gauss-Markov theorem, OLS is BLUE. The Gauss-Markov theorem doesn't mention the normality of errors. If the errors are distributed as per the Laplace distribution,...
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### Quantifying prediction uncertainty using deep ensembles: How to combine Laplace distributions?

For a regression problem, I want to train an ensemble of deep neural networks to predict the labeled output as well as the uncertainty, similar to the approach presented in the paper Simple and ...
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### Independence of real and imaginary part of the product of two independent normal variables

Let $X_1,X_2,Y_1,Y_2$ be iid standard normal variables $N(0,1).$ Let $X=X_1+iX_2,$ $Y=Y_1+iY_2$ and $Z=XY.$ We have : $Z=(X_1Y_1 - X_2Y_2) + i(X_1Y_2 + X_2Y_1).$ From https://en.wikipedia.org/wiki/...
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### What Python library functions can one use to determine if a sample is drawn from a Laplace distribution?

I have some data I suspect is drawn from a Laplace distribution rather than a Gaussian one. I can use the Kolmogrov-Smirnov test and the ability to create Uniform and Gaussian distributions of the ...
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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) + (\...
Suppose I have the likelihood $f(X|\theta)$ of some rich model, where $\theta\in\mathbb{R}^n$, and I have been able to find its maximum, $\hat\theta$. Suppose further that for some $i$, the plot of \$...