Parameter Estimation for Stable Distributions and Their Mixtures
Akaike Information Criterion (AIC)
Perform full stability analysis and export results
Bayesian mixture model using normal components (simplified)
Bayesian Information Criterion (BIC)
Build interpolation functions from McCulloch table
Calculate simplified log-likelihood
Estimate stable distribution parameters using classical ECF regression
Clip values between lower and upper bounds
Compare standard EM and EM with Gibbs sampling using kernel ECF
Compare MLE, ECF, and McCulloch estimators on simulated data
Compare McCulloch, ECF, and MLE methods across parameter configuration...
Compare estimation methods with and without Gibbs sampling
Compute log-likelihood, AIC, and BIC for alpha-stable model
Compute McCulloch quantile ratios from sample data
Compute serial interval from CSV file
Cosine exponential function
Cosine-log-weighted exponential with r^(-alpha) term
Extract magnitude and phase components from ECF
Compute empirical characteristic function
Estimate all stable parameters from empirical characteristic function
Empirical Characteristic Function
Estimate stable parameters using weighted ECF regression
EM algorithm for alpha-stable mixture
EM algorithm for alpha-stable mixture using CDF-based ECF and Gibbs M-...
EM algorithm for mixture of alpha-stable distributions using CDF-based...
EM algorithm for alpha-stable mixture using kernel ECF and Gibbs M-ste...
EM algorithm for mixture of alpha-stable distributions using kernel EC...
EM algorithm for alpha-stable mixture using recursive ECF and Gibbs M-...
EM algorithm for mixture of alpha-stable distributions using recursive...
EM algorithm for alpha-stable mixture using weighted OLS and Gibbs M-s...
EM algorithm for mixture of alpha-stable distributions using weighted ...
EM algorithm for two-component Gaussian mixture
EM algorithm for two-component alpha-stable mixture using MLE
EM algorithm for alpha-stable mixture using a custom estimator
Empirical R0 estimation using growth model
Ensure positive scale parameter
Estimate R0 using maximum likelihood
MLE estimation of R0 using generation time
Estimate alpha and gamma from ECF modulus
Estimate beta and delta from ECF phase
Estimate mixture of two stable distributions
Estimate stable parameters using CDF-based ECF regression
Estimate stable parameters using kernel-based ECF method
Estimate single stable distribution parameters
Estimate stable parameters using method of moments
Estimate stable parameters using recursive ECF method
Estimate stable parameters using weighted OLS on recursive ECF
General eta function
Helper function for eta0 computation
Evaluate estimation method using MSE over multiple trials
Evaluate fit quality using RMSE and log-likelihood
Export analysis report to JSON and Excel
False position method update step
Fast numerical integration using trapezoidal rule
Fit Alpha-Stable Distribution using MLE (L-BFGS-B)
Fit MLE Mixture of Two Stable Distributions
Estimate stable parameters using filtered and weighted ECF regression
Generate samples from a predefined alpha-stable mixture
Generate McCulloch lookup table from simulated stable samples
Simulates a mixture of alpha-stable distributions with randomly sample...
Generate synthetic data from two alpha-stable components
Gibbs sampler for Gaussian mixture model
Log-likelihood gradient with respect to alpha
Log-likelihood gradient with respect to beta
Log-likelihood gradient with respect to delta (scale)
Log-likelihood gradient with respect to omega (location)
Imaginary part of the ECF integral
Integrate imaginary component over
Integrate real component over
Integrate cosine-log-weighted exponential
Integrate cosine exponential
Robust integration helper function
Integrate sine-log-weighted exponential
Integrate sine-r-weighted exponential
Integration wrappers for specific integrands
Integrate sin exponential
KDE bandwidth selection using plugin method
Negative log-likelihood for stable distribution using dstable
Log-likelihood for mixture of stable distributions
Maximum likelihood estimation using Nelder-Mead
Estimate stable parameters using McCulloch lookup
Initialization using McCulloch quantile method
Metropolis-Hastings MCMC for stable mixture clustering
Mixture of two stable PDFs
Simple MLE estimation with default starting values
Mock Gibbs sampling for alpha-stable mixture estimation
Mock lookup for alpha and beta (fallback)
Epanechnikov kernel
Gaussian kernel
Uniform kernel
Negative log-likelihood for single stable distribution
Normalized gradient for alpha parameter Computes the normalized gradie...
Normalized objective for beta parameter
Normalized objective for delta parameter
Normalized objective for omega parameter
Compare EM-estimated mixture with a non-optimized reference model
Plot histogram with normal and stable PDF overlays
Plot effective reproduction number (Re) over time
Plot final fitted mixture of alpha-stable distributions
Compare estimated mixture densities from two methods against the true ...
Plot true vs estimated mixture density
Plot RMSE and Log-Likelihood comparison across methods
Plot mixture fit with individual components
Plot mixture of two alpha-stable distributions
Plot fitted mixture on real dataset
Plot posterior mixture density from MCMC samples
Plot trace of a parameter across MCMC iterations
Plot comparison between normal and stable distributions
QCV statistic for tail heaviness
Robust stable PDF computation
Real part of the ECF integral
Recursive weight function
Estimate stable parameters using robust ECF regression
Robust MLE estimation with multiple starting points
Generate random samples from stable distribution
Compute effective reproduction number Rt
Run all EM-based estimations without Gibbs sampling (CRAN-safe)
Run all EM-based estimations with Gibbs sampling (CRAN-safe)
Safe integration wrapper with multiple fallback strategies
Simple 2-component EM using ECF initialization
Simulate mixture data from alpha-stable components
Sine exponential function
Sine-log-weighted exponential with r^(-alpha) term
Sine-r-weighted exponential function
Sine-weighted exponential with r^alpha term
Calculate skewness and kurtosis
Initialize stable distribution parameters
Test normality using multiple statistical tests
Helper function to unpack parameters
Validate and clip parameters for stable distribution
Wasserstein distance between two mixture distributions
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>.