Lmo - Trimmed L-moments and L-comoments

Unlike the legacy product-moments, the 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 samples or any scipy.stats distribution.
• Full support for trimmed L-moment (TL-moments), e.g. lmo.l_moment(..., trim=(1/137, 3.1416)).
• Generalized Method of L-moments: robust distribution fitting that beats MLE.
• Fast estimation of L-comoment matrices from your multidimensional data or multivariate distribution.
• Goodness-of-fit test, using L-moment or L-moment ratio's.
• Exact (co)variance structure of the sample- and population L-moments.
• Theoretical & empirical influence functions of L-moments & L-ratio's.
• Complete docs, including detailed API reference with usage examples and with mathematical $\TeX$ definitions.
• Clean Pythonic syntax for ease of use.
• Vectorized functions for very fast fitting.
• Fully typed, tested, and tickled.
• Optional Pandas integration.

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. Let's calculate the TL-location and TL-scale of a small amount of samples:

>>> import numpy as np
>>> import lmo
>>> rng = np.random.default_rng(1980)
>>> x = rng.standard_cauchy(96)  # pickle me, Lmo
>>> lmo.l_moment(x, [1, 2], trim=(1, 1)).
array([-0.17937038,  0.68287665])

Now compare with the theoretical standard Cauchy TL-moments:

>>> from scipy.stats import cauchy
>>> cauchy.l_moment([1, 2], trim=(1, 1))
array([0.        , 0.69782723])

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See the documentation for more examples and the API reference.

Roadmap

• Automatic trim-length selection.
• Plotting utilities (deps optional), e.g. for L-moment ratio diagrams.

Installation

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

pip install lmo

Required dependencies

These are automatically installed by your package manager, alongside lmo.

Package	Minimum version
Python	3.10
NumPy	See NEP 29
SciPy	1.9

Optional dependencies

Package	Minimum version	Notes
Pandas	1.4	Installable as lmo[pandas]

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