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

[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?