lmo 0.9.0

L-Moments for robust statistics.

Lmo - Trimmed L-moments and L-comoments

Is your tail too heavy? 
Can't find a moment? 
Are the swans black? 
The distribution pathological?

... then look no further: Lmo's got you covered!

Uniform or multi-dimensional, Lmo can summarize it all with one quick glance!

Unlike the legacy moments, L-moments uniquely describe a probability distribution, and are more robust and efficient. The "L" stands for Linear; it is a linear combination of order statistics. So Lmo is as fast as sorting your samples (in terms of time-complexity).

Key Features:

• Calculates trimmed L-moments and L-comoments, from data or a distribution function.
• Complete support for trimmed L-moment (TL-moments): lmo.l_moment(..., trim=(1 / 137, 3.1416)).
• Fast estimation of L-comoment matrices from your multidimensional data.
• A fully non-parametric scipy.stats-like distribution, lmo.l_rv. It's very efficient, robust, fast, and requires only some L-mo's!
• Exact (co)variance structure of the L-moment estimates.
• Complete docs, including overly complex $\TeX$ spaghetti equations.
• Clean Pythonic syntax for ease of use.
• Vectorized functions for very fast fitting.
• Fully typed, tested, and tickled.

Quick example

Even if your data is pathological like Cauchy, and the L-moments are not defined, the trimmed L-moments (TL-moments) can be used instead:

>>> import numpy as np
>>> import lmo
>>> rng = np.random.default_rng(1980)
>>> x = rng.standard_cauchy(96)  # pickle me, Lmo
>>> x.mean(), x.std()  # don't try this at home
(-1.7113440959133905, 19.573507308373326)
>>> lmo.l_loc(x, trim=(1, 1)), lmo.l_scale(x, (1, 1)) 
(-0.17937038148581977, 0.6828766469913776)

For reference; the theoretical TL-location and TL-scale of the standard Cauchy distribution are $\lambda^{(1, 1)}_{1} = 0$ and $\lambda^{(1, 1)}_2 \approx 0.7$ (Elamir & Seheult, 2003).

---

See the documentation for more examples and the API reference.

Roadmap:

• Add methods to all scipy.stats univariate distributions, for finding the theoretical/population L-mo's.
• Robust distribution fitting, using the (generalized) method of L-moments.
• Theoretical L-moment variance structure calculation.
• A generic goodness-of-fit test.
• Automatic trim-length selection.
• Plotting utilities (deps optional), e.g. for L-moment ratio diagrams.
• Extended multivariate support, e.g. theoretical L-comoments, and L-regression.

Installation

Lmo is on PyPI, so you can do something like:

pip install lmo

Dependencies

• python >= 3.10
• numpy >= 1.22
• scipy >= 1.9

Foundational Literature

• J.R.M. Hosking (1990) – L-moments: Analysis and Estimation of Distributions using Linear Combinations of Order Statistics
• E.A.H. Elamir & A.H. Seheult (2003) – Trimmed L-moments
• E.A.H. Elamir & A.H. Seheult (2004) – Exact variance structure of sample L-moments
• J.R.M. Hosking (2007) – Some theory and practical uses of trimmed L-moments
• R. Serfling & P. Xiao (2007) – A contribution to multivariate L-moments: L-comoment matrices
• W.H. Asquith (2011) – Univariate Distributional Analysis with L-moment Statistics