normalized_objective_beta

Computes the normalized gradient of the log-likelihood with respect to the beta parameter
using the latest values of alpha, delta, and omega stored in global vectors.

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

normalized_objective_beta function

<dl><dt>beta</dt>
<dd>Skewness parameter.</dd>
<dt>X1</dt>
<dd>Numeric vector of observations.</dd>
<dt>L_alpha</dt>
<dd>Vector of alpha values (global memory).</dd>
<dt>L_delta</dt>
<dd>Vector of delta values (global memory).</dd>
<dt>L_omega</dt>
<dd>Vector of omega values (global memory).</dd></dl>

Arguments

Normalized objective for beta parameter — normalized_objective_beta

<dl>

<dt>beta</dt>
<dd>Skewness parameter.</dd>


<dt>X1</dt>
<dd>Numeric vector of observations.</dd>


<dt>L_alpha</dt>
<dd>Vector of alpha values (global memory).</dd>


<dt>L_delta</dt>
<dd>Vector of delta values (global memory).</dd>


<dt>L_omega</dt>
<dd>Vector of omega values (global memory).</dd>

</dl>

normalized_objective_beta: Normalized objective for beta parameter

Description

Usage

Value

Arguments