GeneratedAssembled automatically from moduleDocs.ts. No human has reviewed this page.

ef3m

Concept Overview

Exact Fit of the first 3, 4 or 5 Moments: fits a mixture of two Gaussians by matching sample moments instead of by maximum likelihood. M2N takes the observed moments and searches over the second mean and the mixing probability, solving the remaining parameters analytically at each candidate (iter_4 and iter_5 for the four- and five-moment variants); most_likely_parameters then picks the modal solution across that search. It is fast and derivative-free, which is what makes it usable as an initialiser.

When to Use

Use it when a return or bet-outcome distribution is visibly bimodal — two regimes, or a mixture of trades that ran and trades that were stopped — and you want the components without paying for EM. It is the standard way to obtain the mixture parameters bet_size_reserve needs. Because it works from higher moments it is sensitive to tail estimation noise, so on small samples treat its output as an initialisation for a heavier optimiser rather than a final answer.

Mathematical Foundations

Raw Moment

$m_k=E[X^k]$

Mixture Mean

$\mu=p\mu_1+(1-p)\mu_2$

Usage Examples

Rust

Estimate moments

use openquant::ef3m::centered_moment;

let moments = vec![0.0, 1.0, 0.1, 3.0];
let m3 = centered_moment(&moments, 3);

API Reference

Python API

ef3m.centered_moment
ef3m.raw_moment
ef3m.most_likely_parameters
ef3m.fit_m2n

Rust API

M2N
centered_moment
raw_moment
most_likely_parameters

Risk Notes and Caveats

Use as initialization for more expensive optimizers.
Sensitive to higher-moment estimation noise.