fix fit for Laplace distribution

[salbert83]

The current mle fit for Laplace calculates the mean using the median absolute deviation instead of mean absolute deviation. The former is not MLE. Also, I added functionality for a weighted Laplace MLE.

[codecov-commenter]

Codecov Report

Merging #1309 (857debf) into master (ac372f0) will increase coverage by 0.00%.
The diff coverage is 100.00%.

❗ Current head 857debf differs from pull request most recent head e3c70c0. Consider uploading reports for the commit e3c70c0 to get more accurate results

@@           Coverage Diff           @@
##           master    #1309   +/-   ##
=======================================
  Coverage   81.57%   81.58%           
=======================================
  Files         115      115           
  Lines        6649     6651    +2     
=======================================
+ Hits         5424     5426    +2     
  Misses       1225     1225           

Impacted Files	Coverage Δ
src/univariate/continuous/laplace.jl	92.15% <100.00%> (+0.32%)	⬆️

---

Continue to review full report at Codecov.

Legend - Click here to learn more
Δ = absolute <relative> (impact), ø = not affected, ? = missing data
Powered by Codecov. Last update ac372f0...e3c70c0. Read the comment docs.

[devmotion]

Great, thanks for condensing the PR! One final question: could you check if it is possible to reduce the tolerance in

Distributions.jl/test/fit.jl

Line 361 in ac372f0

@test isapprox(scale(d) , 3.0, atol=0.2)

? I am curious if it is possible to improve the tests which apparently missed this bug.

[salbert83]

Yes, I think reducing the tolerance should catch it. As a minor note, the MLE of the mean for Laplace need not be unique for an even number of samples. I know median does select a unique value. I would use "N+1" in place of "N" for the number of generated values. Then, since there are closed forms for both the location and scale parameters for this distribution and the random seed is fixed, I think a much smaller tolerance would do.

I actually came across this when testing my implementation of the weighted MLE code, which I will put in a separate pull request. Thank you!

[devmotion]

Thanks again, I updated the tests as well.