false_position_update

Performs a single iteration of the false position (regula falsi) method
for root-finding. This method approximates the root of a function by
using a linear interpolation between two points where the function
changes sign.

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

false_position_update function

<dl><dt>a</dt>
<dd>Numeric scalar. Left bound of the interval.</dd>
<dt>b_n</dt>
<dd>Numeric scalar. Right bound of the interval (current step).</dd>
<dt>f_a</dt>
<dd>Numeric scalar. Value of the objective function evaluated at `a`.</dd>
<dt>f_b</dt>
<dd>Numeric scalar. Value of the objective function evaluated at `b_n`.</dd>
<dt>objective_func</dt>
<dd>Function. The objective function whose root is being sought.</dd></dl>

Arguments

False position method update step — false_position_update

<dl>

<dt>a</dt>
<dd>Numeric scalar. Left bound of the interval.</dd>


<dt>b_n</dt>
<dd>Numeric scalar. Right bound of the interval (current step).</dd>


<dt>f_a</dt>
<dd>Numeric scalar. Value of the objective function evaluated at `a`.</dd>


<dt>f_b</dt>
<dd>Numeric scalar. Value of the objective function evaluated at `b_n`.</dd>


<dt>objective_func</dt>
<dd>Function. The objective function whose root is being sought.</dd>

</dl>

false_position_update: False position method update step

Description

Usage

Value

Arguments