generate_mcculloch_table

Simulates alpha-stable samples across a grid of alpha and beta values, and computes
quantile-based ratios used for McCulloch estimation. The result is a lookup table
indexed by (alpha, beta) keys.

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

generate_mcculloch_table function

<dl><dt>alpha_grid</dt>
<dd>Vector of alpha values to simulate.</dd>
<dt>beta_grid</dt>
<dd>Vector of beta values to simulate.</dd>
<dt>size</dt>
<dd>Number of samples per simulation.</dd></dl>

Arguments

Generate McCulloch lookup table from simulated stable samples — generate_mcculloch_table

<dl>

<dt>alpha_grid</dt>
<dd>Vector of alpha values to simulate.</dd>


<dt>beta_grid</dt>
<dd>Vector of beta values to simulate.</dd>


<dt>size</dt>
<dd>Number of samples per simulation.</dd>

</dl>

generate_mcculloch_table: Generate McCulloch lookup table from simulated stable samples

Description

Usage

Value

Arguments