Parameter Estimation for Stable Distributions and Their Mixtures

Documentation for package ‘MixStable’ version 0.1.0

DESCRIPTION file.

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-- A --

aic	Akaike Information Criterion (AIC)
analyse_stable_distribution	Perform full stability analysis and export results

-- B --

bayesian_mixture_model	Bayesian mixture model using normal components (simplified)
bic	Bayesian Information Criterion (BIC)
build_mcculloch_interpolators	Build interpolation functions from McCulloch table

-- C --

calculate_log_likelihood	Calculate simplified log-likelihood
CDF	Estimate stable distribution parameters using classical ECF regression
clip	Clip values between lower and upper bounds
compare_em_vs_em_gibbs	Compare standard EM and EM with Gibbs sampling using kernel ECF
compare_estimators_on_simulations	Compare MLE, ECF, and McCulloch estimators on simulated data
compare_methods_across_configs	Compare McCulloch, ECF, and MLE methods across parameter configurations
compare_methods_with_gibbs	Compare estimation methods with and without Gibbs sampling
compute_model_metrics	Compute log-likelihood, AIC, and BIC for alpha-stable model
compute_quantile_ratios	Compute McCulloch quantile ratios from sample data
compute_serial_interval	Compute serial interval from CSV file
cosine_exp_ralpha	Cosine exponential function
cosine_log_weighted_exp_ralpha	Cosine-log-weighted exponential with r^(-alpha) term

-- D --

DONNEE_with_serial_interval

Example serial interval data

-- E --

ecf_components	Extract magnitude and phase components from ECF
ecf_empirical	Compute empirical characteristic function
ecf_estimate_all	Estimate all stable parameters from empirical characteristic function
ecf_fn	Empirical Characteristic Function
ecf_regression	Estimate stable parameters using weighted ECF regression
empirical_r0	Empirical R0 estimation using growth model
em_alpha_stable	EM algorithm for alpha-stable mixture
em_estimate_stable_from_cdf	EM algorithm for mixture of alpha-stable distributions using CDF-based ECF
em_estimate_stable_from_cdf_with_gibbs	EM algorithm for alpha-stable mixture using CDF-based ECF and Gibbs M-step
em_estimate_stable_kernel_ecf	EM algorithm for mixture of alpha-stable distributions using kernel ECF
em_estimate_stable_kernel_ecf_with_gibbs	EM algorithm for alpha-stable mixture using kernel ECF and Gibbs M-step
em_estimate_stable_recursive_ecf	EM algorithm for mixture of alpha-stable distributions using recursive ECF
em_estimate_stable_recursive_ecf_with_gibbs	EM algorithm for alpha-stable mixture using recursive ECF and Gibbs M-step
em_estimate_stable_weighted_ols	EM algorithm for mixture of alpha-stable distributions using weighted OLS
em_estimate_stable_weighted_ols_with_gibbs	EM algorithm for alpha-stable mixture using weighted OLS and Gibbs M-step
em_estimation_mixture	EM algorithm for two-component Gaussian mixture
em_fit_alpha_stable_mixture	EM algorithm for two-component alpha-stable mixture using MLE
em_stable_mixture	EM algorithm for alpha-stable mixture using a custom estimator
ensure_positive_scale	Ensure positive scale parameter
estimate_alpha_gamma	Estimate alpha and gamma from ECF modulus
estimate_beta_delta	Estimate beta and delta from ECF phase
estimate_mixture_params	Estimate mixture of two stable distributions
estimate_stable_from_cdf	Estimate stable parameters using CDF-based ECF regression
estimate_stable_kernel_ecf	Estimate stable parameters using kernel-based ECF method
estimate_stable_params	Estimate single stable distribution parameters
estimate_stable_r	Estimate stable parameters using method of moments
estimate_stable_recursive_ecf	Estimate stable parameters using recursive ECF method
estimate_stable_weighted_ols	Estimate stable parameters using weighted OLS on recursive ECF
est_r0_ml	Estimate R0 using maximum likelihood
est_r0_mle	MLE estimation of R0 using generation time
eta0	Helper function for eta0 computation
eta_func	General eta function
evaluate_estimation_method	Evaluate estimation method using MSE over multiple trials
evaluate_fit	Evaluate fit quality using RMSE and log-likelihood
export_analysis_report	Export analysis report to JSON and Excel

-- F --

false_position_update	False position method update step
fast_integrate	Fast numerical integration using trapezoidal rule
fit_alpha_stable_mle	Fit Alpha-Stable Distribution using MLE (L-BFGS-B)
fit_mle_mixture	Fit MLE Mixture of Two Stable Distributions
fit_stable_ecf	Estimate stable parameters using filtered and weighted ECF regression

-- G --

generate_alpha_stable_mixture	Generate samples from a predefined alpha-stable mixture
generate_mcculloch_table	Generate McCulloch lookup table from simulated stable samples
generate_mixture_data	Simulates a mixture of alpha-stable distributions with randomly sampled parameters.
generate_synthetic_data	Generate synthetic data from two alpha-stable components
gibbs_sampler	Gibbs sampler for Gaussian mixture model
grad_loglik_alpha	Log-likelihood gradient with respect to alpha
grad_loglik_beta	Log-likelihood gradient with respect to beta
grad_loglik_delta	Log-likelihood gradient with respect to delta (scale)
grad_loglik_omega	Log-likelihood gradient with respect to omega (location)

-- I --

Im	Imaginary part of the ECF integral
integrate_cosine	Integrate cosine exponential
integrate_cosine_log_weighted	Integrate cosine-log-weighted exponential
integrate_function	Robust integration helper function
integrate_sine	Integrate sin exponential
integrate_sine_log_weighted	Integrate sine-log-weighted exponential
integrate_sine_r_weighted	Integrate sine-r-weighted exponential
integrate_sine_weighted	Integration wrappers for specific integrands
Int_Im	Integrate imaginary component over \mathbb{R}
Int_Re	Integrate real component over \mathbb{R}

-- K --

kde_bandwidth_plugin

KDE bandwidth selection using plugin method

-- L --

log_likelihood_mixture	Log-likelihood for mixture of stable distributions
L_stable	Negative log-likelihood for stable distribution using dstable

-- M --

Max_vrai	Maximum likelihood estimation using Nelder-Mead
mcculloch_lookup_estimate	Estimate stable parameters using McCulloch lookup
mcculloch_quantile_init	Initialization using McCulloch quantile method
metropolis_hastings	Metropolis-Hastings MCMC for stable mixture clustering
mixture_stable_pdf	Mixture of two stable PDFs
mle_estimate	Simple MLE estimation with default starting values
mock_gibbs_sampling	Mock Gibbs sampling for alpha-stable mixture estimation
mock_lookup_alpha_beta	Mock lookup for alpha and beta (fallback)

-- N --

negative_log_likelihood	Negative log-likelihood for single stable distribution
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.
normalized_objective_beta	Normalized objective for beta parameter
normalized_objective_delta	Normalized objective for delta parameter
normalized_objective_omega	Normalized objective for omega parameter
N_epanechnikov	Epanechnikov kernel
N_gaussian	Gaussian kernel
N_uniform	Uniform kernel

-- P --

plot_comparison	Compare EM-estimated mixture with a non-optimized reference model
plot_distributions	Plot histogram with normal and stable PDF overlays
plot_effective_reproduction_number	Plot effective reproduction number (Re) over time
plot_final_mixture_fit	Plot final fitted mixture of alpha-stable distributions
plot_fit_vs_true	Plot true vs estimated mixture density
plot_fit_vs_true_methods	Compare estimated mixture densities from two methods against the true density
plot_method_comparison	Plot RMSE and Log-Likelihood comparison across methods
plot_mixture	Plot mixture of two alpha-stable distributions
plot_mixture_fit	Plot mixture fit with individual components
plot_real_mixture_fit	Plot fitted mixture on real dataset
plot_results	Plot posterior mixture density from MCMC samples
plot_trace	Plot trace of a parameter across MCMC iterations
plot_vs_normal_stable	Plot comparison between normal and stable distributions

-- Q --

qcv_stat

QCV statistic for tail heaviness

-- R --

Re	Real part of the ECF integral
recursive_weight	Recursive weight function
robust_ecf_regression	Estimate stable parameters using robust ECF regression
robust_mle_estimate	Robust MLE estimation with multiple starting points
rstable	Generate random samples from stable distribution
RT	Compute effective reproduction number Rt
run_all_estimations	Run all EM-based estimations without Gibbs sampling (CRAN-safe)
run_estimations_with_gibbs	Run all EM-based estimations with Gibbs sampling (CRAN-safe)
r_stable_pdf	Robust stable PDF computation

-- S --

safe_integrate	Safe integration wrapper with multiple fallback strategies
simple_em_real	Simple 2-component EM using ECF initialization
simulate_mixture	Simulate mixture data from alpha-stable components
sine_exp_ralpha	Sine exponential function
sine_log_weighted_exp_ralpha	Sine-log-weighted exponential with r^(-alpha) term
sine_r_weighted_exp_ralpha	Sine-r-weighted exponential function
sine_weighted_exp_ralpha	Sine-weighted exponential with r^alpha term
skew_kurtosis	Calculate skewness and kurtosis
stable_fit_init	Initialize stable distribution parameters

-- T --

TableS2_serial_interval_mean_	Example transmission pair data with mean serial interval
test_normality	Test normality using multiple statistical tests

-- U --

unpack_params

Helper function to unpack parameters

-- V --

validate_params

Validate and clip parameters for stable distribution

-- W --

wasserstein_distance_mixture

Wasserstein distance between two mixture distributions