Let X distributed as Laplace distribution with (a,b) where a , b are the location and scale parameter respectively. If we want to estimate the scale parameter (b) we can assume that one of:
1. The location parameter is a constant and known
2. The location parameter is unknown so, we can use median as an estimator of the location (median is the Maximum-likelihood estimator for location of Laplace distribution) then, derive the scale estimator for laplace distribution.
Do you have another approach or suggestion please.?
Thank you in advance for any help you can provide!
Dear Huda
The maximum likelihood estimatior of the scale, is the average of the absolute deviation from the random variables and the median of the sample (the maximum likelihood estimatior of the location parameter). See http://en.wikipedia.org/wiki/Laplace_distribution.
I hope this help.
Dear Huda
The maximum likelihood estimatior of the scale, is the average of the absolute deviation from the random variables and the median of the sample (the maximum likelihood estimatior of the location parameter). See http://en.wikipedia.org/wiki/Laplace_distribution.
I hope this help.
Ass Guillermo proposed by ML. There also exists a R package which can help you:
http://cran.r-project.org/web/packages/NormalLaplace/NormalLaplace.pdf
Guillermo is right. I used the Laplace for modelling log-return in poker per hour of play with sample median as location.
I agree, MLE will give the required result. I think R software will need a data set or simulation before you can get the estimates.
Dear Huda,
You can estimate the location and scale parameter of Laplace distribution by using the Bayesian approach. It is easy to find the full conditional distributions for all parameters by representing the Laplace distribution as a scale mixture of normals family with suitable priors for the parameters. Then you can use the Gibbs sampler to update the parameters from the posterior.
In linear regression model, I have estimated the location and scale parameters for the general case of Laplace distribution which is called the asymmetric Laplace distribution in my paper "Model selection in quantile regression
models "
http://www.tandfonline.com/doi/abs/10.1080/02664763.2014.959905?journalCode=cjas20#.VNwATfmUeWU
Hope this helps
Dear Rahim,
Many thanks for your attention.
I have many papers about bayesian estimation for the scale parameter of Laplace distribution (some times called double exponential distribution), but I always assumed that, the location parameter is known.
Now, I want to estimate the scale parameter of Laplace distribution using Bayesian approach with assuming the location parameter is unknown and I will replace median sample instead of location parameter in monte-carlo simulation. Is there another suggestion about the location parameter when we want estimate scale parameter?
I'm so grateful for all.
Dear Huda, as many people answered you can use maximum likelihood estimator. Such can of estimators are well estimated in python or R languages. If still need I can provide a sample script with python adapted to your data if you can provide me with it. There is also the possibility to establish scale and shape factor using Excel + Solver. We need to implement the Laplace distribution our self but then it will be easy to use the solver plug in to find the parameters.
Many thanks for all. Dear Efraín, median is the maximum likelihood estimator for the location of Laplace distribution. See this URL please
http://math.stackexchange.com/questions/240496/finding-the-maximum-likelihood-estimator
Actually, many samples (many thousand) are generated from Laplace distribution using Monte-carlo simulation. The estimates that under study are computed from each sample and compared empirically using Monte carlo simulation. The performance of these estimators is studied depending on the mean square errors (MSE's).
Best Regards
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