jorenham / Lmo

Trimmed L-moments and L-comoments for robust statistics.

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

Dependencies

These are automatically installed by your package manager when installing Lmo.

Package	Supported versions
Python	>=3.10
NumPy	>=1.23
SciPy	>=1.9

Additionally, Lmo supports the following optional packages:

Package	Supported versions	Installation
Pandas	>=1.5	pip install Lmo[pandas]

See SPEC 0 for more information.

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
• 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