normalized_grad_alpha

Normalized gradient for alpha parameter
Computes the normalized gradient of the log-likelihood with respect to the alpha parameter
over a set of observations. This is useful for optimization routines where scale-invariant
updates are preferred.

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_grad_alpha function

<dl><dt>alpha</dt>
<dd>Stability parameter.</dd>
<dt>beta</dt>
<dd>Skewness parameter.</dd>
<dt>delta</dt>
<dd>Scale parameter.</dd>
<dt>omega</dt>
<dd>Location parameter.</dd>
<dt>x</dt>
<dd>Numeric vector of observations.</dd></dl>

Arguments

Normalized gradient for alpha parameter
Computes the normalized gradient of the log-likelihood with respect to the alpha parameter
over a set of observations. This is useful for optimization routines where scale-invariant
updates are preferred. — normalized_grad_alpha

<dl>

<dt>alpha</dt>
<dd>Stability parameter.</dd>


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


<dt>delta</dt>
<dd>Scale parameter.</dd>


<dt>omega</dt>
<dd>Location parameter.</dd>


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

</dl>

Normalized gradient for alpha parameter
Computes the normalized gradient of the log-likelihood with respect to the alpha parameter
over a set of observations. This is useful for optimization routines where scale-invariant
updates are preferred.

normalized_grad_alpha: Normalized gradient for alpha parameter Computes the normalized gradient of the log-likelihood with respect to the alpha parameter over a set of observations. This is useful for optimization routines where scale-invariant updates are preferred.

Description

Usage

Value

Arguments