estimate_beta_delta

Estimate beta and delta from ECF phase

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

estimate_beta_delta function

<dl><dt>t_grid</dt>
<dd>Vector of frequency values.</dd>
<dt>phi_vals</dt>
<dd>Complex vector of ECF values.</dd>
<dt>alpha_hat</dt>
<dd>Estimated alpha.</dd>
<dt>gamma_hat</dt>
<dd>Estimated gamma.</dd>
<dt>weights</dt>
<dd>Optional vector of weights.</dd></dl>

Arguments

Estimate beta and delta from ECF phase — estimate_beta_delta

<dl>

<dt>t_grid</dt>
<dd>Vector of frequency values.</dd>


<dt>phi_vals</dt>
<dd>Complex vector of ECF values.</dd>


<dt>alpha_hat</dt>
<dd>Estimated alpha.</dd>


<dt>gamma_hat</dt>
<dd>Estimated gamma.</dd>


<dt>weights</dt>
<dd>Optional vector of weights.</dd>

</dl>

estimate_beta_delta: Estimate beta and delta from ECF phase

Description

Usage

Value

Arguments