safe_integrate

Performs numerical integration with progressively more conservative
settings to improve robustness. Useful when standard integration
may fail due to oscillatory or heavy-tailed functions.

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

safe_integrate function

<dl><dt>integrand_func</dt>
<dd>Function to integrate. Must accept a numeric vector
as input and return numeric values.</dd>
<dt>lower</dt>
<dd>Numeric scalar. Lower bound of the integration interval
(default = 1e-8 to avoid singularities at 0).</dd>
<dt>upper</dt>
<dd>Numeric scalar. Upper bound of the integration interval
(default = 50).</dd>
<dt>max_attempts</dt>
<dd>Integer. Maximum number of fallback attempts with
modified settings if the initial integration fails.</dd>
<dt>...</dt>
<dd>Additional arguments passed to <code>integrand_func</code>.</dd></dl>

Arguments

Safe integration wrapper with multiple fallback strategies — safe_integrate

<dl>

<dt>integrand_func</dt>
<dd>Function to integrate. Must accept a numeric vector
as input and return numeric values.</dd>


<dt>lower</dt>
<dd>Numeric scalar. Lower bound of the integration interval
(default = 1e-8 to avoid singularities at 0).</dd>


<dt>upper</dt>
<dd>Numeric scalar. Upper bound of the integration interval
(default = 50).</dd>


<dt>max_attempts</dt>
<dd>Integer. Maximum number of fallback attempts with
modified settings if the initial integration fails.</dd>


<dt>...</dt>
<dd>Additional arguments passed to <code>integrand_func</code>.</dd>

</dl>

safe_integrate: Safe integration wrapper with multiple fallback strategies

Description

Usage

Value

Arguments