metropolis_hastings

Performs Metropolis-Hastings sampling to estimate parameters of a two-component
alpha-stable mixture model. Proposals are generated for each parameter and accepted
based on likelihood ratios. Cluster assignments are updated at each iteration.

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

metropolis_hastings function

<dl><dt>fct</dt>
<dd>Function to estimate initial parameters.</dd>
<dt>iterations</dt>
<dd>Number of MCMC iterations.</dd>
<dt>lok</dt>
<dd>Numeric vector of observations.</dd>
<dt>aa</dt>
<dd>Prior parameters for Dirichlet distribution.</dd>
<dt>proposal_std</dt>
<dd>Standard deviation for proposal distributions.</dd></dl>

Arguments

Metropolis-Hastings MCMC for stable mixture clustering — metropolis_hastings

<dl>

<dt>fct</dt>
<dd>Function to estimate initial parameters.</dd>


<dt>iterations</dt>
<dd>Number of MCMC iterations.</dd>


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


<dt>aa</dt>
<dd>Prior parameters for Dirichlet distribution.</dd>


<dt>proposal_std</dt>
<dd>Standard deviation for proposal distributions.</dd>

</dl>

metropolis_hastings: Metropolis-Hastings MCMC for stable mixture clustering

Description

Usage

Value

Arguments