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I have a dataset where I suspect the residuals are approximately Laplace-distributed.

There are three continuous predictors. When I split up the data into many bins, based on the values of these predictors, and plot the density for each subset, it seems to me that the data is always centered at 0, but lower values of the predictors lead to wide laplace densities and higher values lead to narrower laplace densities.

My intuition is to use some kind of linear regression where the dispersion, rather than the mean, is modeled.

  1. Can a GLM handle the situation where the residuals are laplace-distributed?
  2. Is there a mature package in R that can do this? Seems like stats::glm cannot.
  3. I am familiar with the DGLM (double generalized linear model), so I suspect if I could overcome 1 and 2 I could do something to model the dispersion.
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  • $\begingroup$ My feeling is that gamlss can do that. You can specifically model the scale and location separately. The accompanying package gamlss.dist includes the Laplace distribution via PE. $\endgroup$
    – COOLSerdash
    Commented Oct 18, 2018 at 15:17
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    $\begingroup$ These wouldn't happen to be stock returns or similar financial data, would they? $\endgroup$
    – Glen_b
    Commented Oct 20, 2018 at 5:08

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