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Example notebook that shows L-moments > product-moments for measuring scale #313

@jorenham

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@jorenham

E.g. sample estimator bias for small n (which still is the case when the std is debiased

Show how the normal distribution pdf cleans up when L-scale is used to standardize.

Showing the effects of heavy tails and outliers is (also) low-hanging fruit.

Compare:

  • Sample STD (debiasing it might be a nice flex)
  • Mean absolute deviation (maybe)
  • MAD (median absolute deviation)
  • IQR (inter-quartile range)
  • L-scale
  • TL-scale

It might be worth mentioning that IQR is also an L-statistic like L-moments are (MAD isn't, but median is)

Distributions:

  • uniform (i.e. the simplest polynomial, and the L-moment's "base distribution")
  • normal (do the disappearance trick of sqrt(pi))
  • logistic (l2==1 is a nice flex)
  • t (df = 2 or 3)
  • log-normal?

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