em_alpha_stable

Estimates parameters of an alpha-stable mixture using EM with optional random initialization.

Provides various functions for parameter estimation of one-dimensional
stable distributions and their mixtures. It implements a diverse set of
estimation methods, including quantile-based approaches, regression methods
based on the empirical characteristic function (empirical, kernel, and
recursive), and maximum likelihood estimation. For mixture models, it provides
stochastic expectation–maximization (SEM) algorithms and Bayesian estimation
methods using sampling and importance sampling to overcome the long burn-in
period of Markov Chain Monte Carlo (MCMC) strategies. The package also includes
tools and statistical tests for analyzing whether a dataset follows a stable
distribution. Some of the implemented methods are described in
Hajjaji, O., Manou-Abi, S. M., and Slaoui, Y. (2024) <doi:10.1080/02664763.2024.2434627>.

Solym Manou-Abi

MixStable

Parameter Estimation for Stable Distributions and Their Mixtures

Adam Najib

Yousri Slaoui

em_alpha_stable function

<dl><dt>data</dt>
<dd>Numeric vector of observations.</dd>
<dt>n_components</dt>
<dd>Integer. Number of mixture components.</dd>
<dt>max_iter</dt>
<dd>Integer. Maximum number of EM iterations.</dd>
<dt>tol</dt>
<dd>Numeric. Convergence tolerance.</dd>
<dt>random_init</dt>
<dd>Logical. Whether to use random initialization.</dd>
<dt>debug</dt>
<dd>Logical. Whether to print debug information.</dd></dl>

Arguments

EM algorithm for alpha-stable mixture — em_alpha_stable

<dl>

<dt>data</dt>
<dd>Numeric vector of observations.</dd>


<dt>n_components</dt>
<dd>Integer. Number of mixture components.</dd>


<dt>max_iter</dt>
<dd>Integer. Maximum number of EM iterations.</dd>


<dt>tol</dt>
<dd>Numeric. Convergence tolerance.</dd>


<dt>random_init</dt>
<dd>Logical. Whether to use random initialization.</dd>


<dt>debug</dt>
<dd>Logical. Whether to print debug information.</dd>

</dl>

em_alpha_stable: EM algorithm for alpha-stable mixture

Description

Usage

Value

Arguments