Talk:Laplace distribution

You write: "The difference between two independent identically distributed exponential random variables is governed by a Laplace distribution." How exactly? Can you give the pdf-function of the Laplace distribution in tems of lambda, where lambda is the parameter of the exponential distribution (f(t) = lambda*exp(-lambda*t)?


 * The Laplace distribution is the distribution of the difference of two random variables (rv) each with an exponential distribution.


 * Let X be one of the rvs and let Y be the other. X is distributed with a pdf of (f(t) = lambda*exp(-lambda*t) and Y is distributed with a pdf of (f(t) = gamma*exp(-gamma*t). Then the rv (X - Y) is distributed as a Laplace distribution.


 * If gamma == lambda then the Laplace distribution is symmetric (a classical Laplace distribution); if gamma != lambda then X - Y is distributed as skew symmetric Laplace distribution.


 * Hope that helps.DrMicro (talk) 19:06, 10 January 2012 (UTC)

Integration to the CDF
In the section on finding the Laplace CDF someone writes, "The Laplace distribution is easy to integrate (if one distinguishes two symmetric cases) due to the use of the absolute value function". I find this to be disingenuous and even a little snarky. Frankly it sounds a bit like many texts and college math instructors I've encountered, where we simply hand-wave over the work leaving many (like myself) searching for hours for the correct answer (THANKS!). A simple integration does not work here. See https://math.stackexchange.com/questions/1632328/cdf-for-laplace-distribution for more information, and a possible solution. — Preceding unsigned comment added by 2600:8800:9280:E0B:AC70:C810:7DC0:DF44 (talk) 22:58, 13 September 2020 (UTC)

Redirect page needed
Can someone add a redirect from Laplace Distribution with capital letters? —The preceding unsigned comment was added by 82.211.86.2 (talk) 16:22, 11 January 2007 (UTC).

Entropy calculation
It should be better to let the $$\ln(2eb)$$ instead of the $$\log(2eb)$$ because someone don't know that $$\log$$ is equal to $$\ln$$.

Rounding error?
Is a Laplace distribution what one would expect for rounding error due to limited numerical precision? —Ben FrantzDale (talk) 19:01, 7 February 2008 (UTC)

Maximum Likelihood Estimation
Isn't the median of the data also the maximum likelihood estimator for the location parameter (mean)? Shouldn't this be stated or did I miss it? Fjhickernell (talk) 01:26, 18 February 2010 (UTC)
 * I think the median already notes that the sample median is the MLE for the location parameter, and gives the formula for the MLE of b. But if it isn't clear, then perhaps it should be edited to clarify. Rlendog (talk) 01:59, 18 February 2010 (UTC)

Double-Sided Deleted
All of the previous work on the double-sided is now gone. Please add it back. — Preceding unsigned comment added by 75.66.94.27 (talk) 16:03, 23 February 2013 (UTC)

PDF b<1
http://www.math.uah.edu/stat/special/Laplace.html

Do not divide by b — Preceding unsigned comment added by 75.66.94.27 (talk) 16:21, 23 February 2013 (UTC)

Generation of a sample of Laplace random variables
The equation provided for generating a sample of Laplace-distributed random variables does not seem to provide the desired sample. The method described here ... http://www.math.uah.edu/stat/special/Laplace.html ... seems to work better. ... In "matlab" ...  U = rand(r,c); in = find(U<=0.5); ip = find(U>0.5); x(in) = muX + sigmaX/sr2 * log(2*U(in)); x(ip) = muX - sigmaX/sr2 * log(2*(1-U(ip)));

Related distributions
I've the idea in this section it is forgotten to mention the independence of the varables.82.75.155.228 (talk) 19:53, 6 September 2014 (UTC)

Information on the uncertainty of the location estimate
tomaschwutz (talk) 10:54, 24 January 2017 (UTC)
 * practitioners dealing with Laplace distributed samples are interested in confidence intervals on the estimate of the location parameter
 * Lawrence 2013 in Open Journal of Statistics (doi=10.4236/ojs.2013.36050) gives a formula for the cumulative density of the location of a one-parameter-form of the Laplace distribtution
 * To the statistitians: Is it possible to use these formulas to compute 95% confidence intervals on the location estimate given sample x?
 * If so, could an explained example be added to this wiki-page?
 * If there is a reliable source for constructing the confidence interval that can certainly be added to the parameter estimation section. Does Lawrence provide that formula?  Or if not, are you aware of a source that does? Rlendog (talk) 15:25, 24 January 2017 (UTC)

Fisher Information?
Most distributions have Fisher Information on the right panel. I don't see it for this one. I believe that it exists for the Laplace. Is there a reason it is not on here? — Preceding unsigned comment added by 96.56.198.67 (talk) 19:34, 30 January 2019 (UTC)

Probability density functions plots
The plots are clearly wrong, as e^0=1 not 0.45, can someone replace them? wolfRAMM 18:41, 17 February 2022 (UTC)

-- This is the Octave code to test the MAD and the kurtosis: A=1; B=1e6; x=sqrt(exprnd(1,A,B)).*randn(A,B)*sqrt(2); assert(mean(abs(x)),1,1e-2); assert(kurtosis(x),6,1e-1); — Preceding unsigned comment added by Gab27183 (talk • contribs) 11:08, 6 March 2024 (UTC)