{ "_id": "6a1d5d9e1d7bb097a0a48ccf", "Package": "MixStable", "Type": "Package", "Title": "Parameter Estimation for Stable Distributions and Their Mixtures", "Version": "0.1.0", "Authors@R": "c(\nperson(\"Solym\", \"Manou-Abi\", email = \"solym.manou.abi@univ-poitiers.fr\", role = c(\"aut\", \"cre\")),\nperson(\"Adam\", \"Najib\", email = \"najibadam145@gmail.com\", role = \"aut\"),\nperson(\"Yousri\", \"Slaoui\", email = \"Yousri.Slaoui@math.univ-poitiers.fr\", role = \"aut\"))", "Description": "Provides various functions for parameter estimation of\none-dimensional stable distributions and their mixtures. It\nimplements a diverse set of estimation methods, including\nquantile-based approaches, regression methods based on the\nempirical characteristic function (empirical, kernel, and\nrecursive), and maximum likelihood estimation. For mixture\nmodels, it provides stochastic expectation–maximization (SEM)\nalgorithms and Bayesian estimation methods using sampling and\nimportance sampling to overcome the long burn-in period of\nMarkov Chain Monte Carlo (MCMC) strategies. The package also\nincludes tools and statistical tests for analyzing whether a\ndataset follows a stable distribution. Some of the implemented\nmethods are described in Hajjaji, O., Manou-Abi, S. M., and\nSlaoui, Y. (2024) .", "License": "GPL-3", "Encoding": "UTF-8", "RoxygenNote": "7.3.2", "Config/testthat/edition": "3", "NeedsCompilation": "no", "Packaged": { "Date": "2026-06-01 10:17:48 UTC", "User": "root" }, "Author": "Solym Manou-Abi [aut, cre], Adam Najib [aut], Yousri Slaoui\n[aut]", "Maintainer": "Solym Manou-Abi ", "Repository": "https://cran.r-universe.dev", "Date/Publication": "2025-11-03 19:20:18 UTC", "RemoteUrl": "https://github.com/cran/MixStable", "RemoteRef": "HEAD", "RemoteSha": "d869cc7ba6913ffb48f211b359d2593b30b85d26", "MD5sum": "fc3484b69078f0860a005428f3f65ea9", "_user": "cran", "_type": "src", "_file": "MixStable_0.1.0.tar.gz", "_fileid": "7e46aa3ffb77e3866c17cdedb5c3127aa4ecc6c21e84ec3400f0ff3f2cbb49f2", "_filesize": 349210, "_sha256": "7e46aa3ffb77e3866c17cdedb5c3127aa4ecc6c21e84ec3400f0ff3f2cbb49f2", "_created": "2026-06-01T10:17:48.000Z", "_published": "2026-06-01T10:23:26.165Z", "_distro": "noble", "_jobs": [ { "job": 78831688530, "time": 288, "config": 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"rows": 1001, "table": true, "tojson": true } ], "_help": [ { "page": "aic", "title": "Akaike Information Criterion (AIC)", "topics": [ "aic" ] }, { "page": "analyse_stable_distribution", "title": "Perform full stability analysis and export results", "topics": [ "analyse_stable_distribution" ] }, { "page": "bayesian_mixture_model", "title": "Bayesian mixture model using normal components (simplified)", "topics": [ "bayesian_mixture_model" ] }, { "page": "bic", "title": "Bayesian Information Criterion (BIC)", "topics": [ "bic" ] }, { "page": "build_mcculloch_interpolators", "title": "Build interpolation functions from McCulloch table", "topics": [ "build_mcculloch_interpolators" ] }, { "page": "calculate_log_likelihood", "title": "Calculate simplified log-likelihood", "topics": [ "calculate_log_likelihood" ] }, { "page": "CDF", "title": "Estimate stable distribution parameters using classical ECF regression", "topics": [ "CDF" ] }, { "page": "clip", "title": "Clip values between lower and upper bounds", "topics": [ "clip" ] }, { "page": "compare_em_vs_em_gibbs", "title": "Compare standard EM and EM with Gibbs sampling using kernel ECF", "topics": [ "compare_em_vs_em_gibbs" ] }, { "page": "compare_estimators_on_simulations", "title": "Compare MLE, ECF, and McCulloch estimators on simulated data", "topics": [ "compare_estimators_on_simulations" ] }, { "page": "compare_methods_across_configs", "title": "Compare McCulloch, ECF, and MLE methods across parameter configurations", "topics": [ "compare_methods_across_configs" ] }, { "page": "compare_methods_with_gibbs", "title": "Compare estimation methods with and without Gibbs sampling", "topics": [ "compare_methods_with_gibbs" ] }, { "page": "compute_model_metrics", "title": "Compute log-likelihood, AIC, and BIC for alpha-stable model", "topics": [ "compute_model_metrics" ] }, { "page": "compute_quantile_ratios", "title": "Compute McCulloch quantile ratios from sample data", "topics": [ "compute_quantile_ratios" ] }, { "page": "compute_serial_interval", "title": "Compute serial interval from CSV file", "topics": [ "compute_serial_interval" ] }, { "page": "cosine_exp_ralpha", "title": "Cosine exponential function", "topics": [ "cosine_exp_ralpha" ] }, { "page": "cosine_log_weighted_exp_ralpha", "title": "Cosine-log-weighted exponential with r^(-alpha) term", "topics": [ "cosine_log_weighted_exp_ralpha" ] }, { "page": "DONNEE_with_serial_interval", "title": "Example serial interval data", "topics": [ "DONNEE_with_serial_interval" ] }, { "page": "ecf_components", "title": "Extract magnitude and phase components from ECF", "topics": [ "ecf_components" ] }, { "page": "ecf_empirical", "title": "Compute empirical characteristic function", "topics": [ "ecf_empirical" ] }, { "page": "ecf_estimate_all", "title": "Estimate all stable parameters from empirical characteristic function", "topics": [ "ecf_estimate_all" ] }, { "page": "ecf_fn", "title": "Empirical Characteristic Function", "topics": [ "ecf_fn" ] }, { "page": "ecf_regression", "title": "Estimate stable parameters using weighted ECF regression", "topics": [ "ecf_regression" ] }, { "page": "em_alpha_stable", "title": "EM algorithm for alpha-stable mixture", "topics": [ "em_alpha_stable" ] }, { "page": "em_estimate_stable_from_cdf", "title": "EM algorithm for mixture of alpha-stable distributions using CDF-based ECF", "topics": [ "em_estimate_stable_from_cdf" ] }, { "page": "em_estimate_stable_from_cdf_with_gibbs", "title": "EM algorithm for alpha-stable mixture using CDF-based ECF and Gibbs M-step", "topics": [ "em_estimate_stable_from_cdf_with_gibbs" ] }, { "page": "em_estimate_stable_kernel_ecf", "title": "EM algorithm for mixture of alpha-stable distributions using kernel ECF", "topics": [ "em_estimate_stable_kernel_ecf" ] }, { "page": "em_estimate_stable_kernel_ecf_with_gibbs", "title": "EM algorithm for alpha-stable mixture using kernel ECF and Gibbs M-step", "topics": [ "em_estimate_stable_kernel_ecf_with_gibbs" ] }, { "page": "em_estimate_stable_recursive_ecf", "title": "EM algorithm for mixture of alpha-stable distributions using recursive ECF", "topics": [ "em_estimate_stable_recursive_ecf" ] }, { "page": "em_estimate_stable_recursive_ecf_with_gibbs", "title": "EM algorithm for alpha-stable mixture using recursive ECF and Gibbs M-step", "topics": [ "em_estimate_stable_recursive_ecf_with_gibbs" ] }, { "page": "em_estimate_stable_weighted_ols", "title": "EM algorithm for mixture of alpha-stable distributions using weighted OLS", "topics": [ "em_estimate_stable_weighted_ols" ] }, { "page": "em_estimate_stable_weighted_ols_with_gibbs", "title": "EM algorithm for alpha-stable mixture using weighted OLS and Gibbs M-step", "topics": [ "em_estimate_stable_weighted_ols_with_gibbs" ] }, { "page": "em_estimation_mixture", "title": "EM algorithm for two-component Gaussian mixture", "topics": [ "em_estimation_mixture" ] }, { "page": "em_fit_alpha_stable_mixture", "title": "EM algorithm for two-component alpha-stable mixture using MLE", "topics": [ "em_fit_alpha_stable_mixture" ] }, { "page": "em_stable_mixture", "title": "EM algorithm for alpha-stable mixture using a custom estimator", "topics": [ "em_stable_mixture" ] }, { "page": "empirical_r0", "title": "Empirical R0 estimation using growth model", "topics": [ "empirical_r0" ] }, { "page": "ensure_positive_scale", "title": "Ensure positive scale parameter", "topics": [ "ensure_positive_scale" ] }, { "page": "est_r0_ml", "title": "Estimate R0 using maximum likelihood", "topics": [ "est_r0_ml" ] }, { "page": "est_r0_mle", "title": "MLE estimation of R0 using generation time", "topics": [ "est_r0_mle" ] }, { "page": "estimate_alpha_gamma", "title": "Estimate alpha and gamma from ECF modulus", "topics": [ "estimate_alpha_gamma" ] }, { "page": "estimate_beta_delta", "title": "Estimate beta and delta from ECF phase", "topics": [ "estimate_beta_delta" ] }, { "page": "estimate_mixture_params", "title": "Estimate mixture of two stable distributions", "topics": [ "estimate_mixture_params" ] }, { "page": "estimate_stable_from_cdf", "title": "Estimate stable parameters using CDF-based ECF regression", "topics": [ "estimate_stable_from_cdf" ] }, { "page": "estimate_stable_kernel_ecf", "title": "Estimate stable parameters using kernel-based ECF method", "topics": [ "estimate_stable_kernel_ecf" ] }, { "page": "estimate_stable_params", "title": "Estimate single stable distribution parameters", "topics": [ "estimate_stable_params" ] }, { "page": "estimate_stable_r", "title": "Estimate stable parameters using method of moments", "topics": [ "estimate_stable_r" ] }, { "page": "estimate_stable_recursive_ecf", "title": "Estimate stable parameters using recursive ECF method", "topics": [ "estimate_stable_recursive_ecf" ] }, { "page": "estimate_stable_weighted_ols", "title": "Estimate stable parameters using weighted OLS on recursive ECF", "topics": [ "estimate_stable_weighted_ols" ] }, { "page": "eta_func", "title": "General eta function", "topics": [ "eta_func" ] }, { "page": "eta0", "title": "Helper function for eta0 computation", "topics": [ "eta0" ] }, { "page": "evaluate_estimation_method", "title": "Evaluate estimation method using MSE over multiple trials", "topics": [ "evaluate_estimation_method" ] }, { "page": "evaluate_fit", "title": "Evaluate fit quality using RMSE and log-likelihood", "topics": [ "evaluate_fit" ] }, { "page": "export_analysis_report", "title": "Export analysis report to JSON and Excel", "topics": [ "export_analysis_report" ] }, { "page": "false_position_update", "title": "False position method update step", "topics": [ "false_position_update" ] }, { "page": "fast_integrate", "title": "Fast numerical integration using trapezoidal rule", "topics": [ "fast_integrate" ] }, { "page": "fit_alpha_stable_mle", "title": "Fit Alpha-Stable Distribution using MLE (L-BFGS-B)", "topics": [ "fit_alpha_stable_mle" ] }, { "page": "fit_mle_mixture", "title": "Fit MLE Mixture of Two Stable Distributions", "topics": [ "fit_mle_mixture" ] }, { "page": "fit_stable_ecf", "title": "Estimate stable parameters using filtered and weighted ECF regression", "topics": [ "fit_stable_ecf" ] }, { "page": "generate_alpha_stable_mixture", "title": "Generate samples from a predefined alpha-stable mixture", "topics": [ "generate_alpha_stable_mixture" ] }, { "page": "generate_mcculloch_table", "title": "Generate McCulloch lookup table from simulated stable samples", "topics": [ "generate_mcculloch_table" ] }, { "page": "generate_mixture_data", "title": "Simulates a mixture of alpha-stable distributions with randomly sampled parameters.", "topics": [ "generate_mixture_data" ] }, { "page": "generate_synthetic_data", "title": "Generate synthetic data from two alpha-stable components", "topics": [ "generate_synthetic_data" ] }, { "page": "gibbs_sampler", "title": "Gibbs sampler for Gaussian mixture model", "topics": [ "gibbs_sampler" ] }, { "page": "grad_loglik_alpha", "title": "Log-likelihood gradient with respect to alpha", "topics": [ "grad_loglik_alpha" ] }, { "page": "grad_loglik_beta", "title": "Log-likelihood gradient with respect to beta", "topics": [ "grad_loglik_beta" ] }, { "page": "grad_loglik_delta", "title": "Log-likelihood gradient with respect to delta (scale)", "topics": [ "grad_loglik_delta" ] }, { "page": "grad_loglik_omega", "title": "Log-likelihood gradient with respect to omega (location)", "topics": [ "grad_loglik_omega" ] }, { "page": "Im", "title": "Imaginary part of the ECF integral", "topics": [ "Im" ] }, { "page": "Int_Im", "title": "Integrate imaginary component over \\mathbb{R}", "topics": [ "Int_Im" ] }, { "page": "Int_Re", "title": "Integrate real component over \\mathbb{R}", "topics": [ "Int_Re" ] }, { "page": "integrate_cosine", "title": "Integrate cosine exponential", "topics": [ "integrate_cosine" ] }, { "page": "integrate_cosine_log_weighted", "title": "Integrate cosine-log-weighted exponential", "topics": [ "integrate_cosine_log_weighted" ] }, { "page": "integrate_function", "title": "Robust integration helper function", "topics": [ "integrate_function" ] }, { "page": "integrate_sine", "title": "Integrate sin exponential", "topics": [ "integrate_sine" ] }, { "page": "integrate_sine_log_weighted", "title": "Integrate sine-log-weighted exponential", "topics": [ "integrate_sine_log_weighted" ] }, { "page": "integrate_sine_r_weighted", "title": "Integrate sine-r-weighted exponential", "topics": [ "integrate_sine_r_weighted" ] }, { "page": "integrate_sine_weighted", "title": "Integration wrappers for specific integrands", "topics": [ "integrate_sine_weighted" ] }, { "page": "kde_bandwidth_plugin", "title": "KDE bandwidth selection using plugin method", "topics": [ "kde_bandwidth_plugin" ] }, { "page": "L_stable", "title": "Negative log-likelihood for stable distribution using dstable", "topics": [ "L_stable" ] }, { "page": "log_likelihood_mixture", "title": "Log-likelihood for mixture of stable distributions", "topics": [ "log_likelihood_mixture" ] }, { "page": "Max_vrai", "title": "Maximum likelihood estimation using Nelder-Mead", "topics": [ "Max_vrai" ] }, { "page": "mcculloch_lookup_estimate", "title": "Estimate stable parameters using McCulloch lookup", "topics": [ "mcculloch_lookup_estimate" ] }, { "page": "mcculloch_quantile_init", "title": "Initialization using McCulloch quantile method", "topics": [ "mcculloch_quantile_init" ] }, { "page": "metropolis_hastings", "title": "Metropolis-Hastings MCMC for stable mixture clustering", "topics": [ "metropolis_hastings" ] }, { "page": "mixture_stable_pdf", "title": "Mixture of two stable PDFs", "topics": [ "mixture_stable_pdf" ] }, { "page": "mle_estimate", "title": "Simple MLE estimation with default starting values", "topics": [ "mle_estimate" ] }, { "page": "mock_gibbs_sampling", "title": "Mock Gibbs sampling for alpha-stable mixture estimation", "topics": [ "mock_gibbs_sampling" ] }, { "page": "mock_lookup_alpha_beta", "title": "Mock lookup for alpha and beta (fallback)", "topics": [ "mock_lookup_alpha_beta" ] }, { "page": "N_epanechnikov", "title": "Epanechnikov kernel", "topics": [ "N_epanechnikov" ] }, { "page": "N_gaussian", "title": "Gaussian kernel", "topics": [ "N_gaussian" ] }, { "page": "N_uniform", "title": "Uniform kernel", "topics": [ "N_uniform" ] }, { "page": "negative_log_likelihood", "title": "Negative log-likelihood for single stable distribution", "topics": [ "negative_log_likelihood" ] }, { "page": "normalized_grad_alpha", "title": "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.", "topics": [ "normalized_grad_alpha" ] }, { "page": "normalized_objective_beta", "title": "Normalized objective for beta parameter", "topics": [ "normalized_objective_beta" ] }, { "page": "normalized_objective_delta", "title": "Normalized objective for delta parameter", "topics": [ "normalized_objective_delta" ] }, { "page": "normalized_objective_omega", "title": "Normalized objective for omega parameter", "topics": [ "normalized_objective_omega" ] }, { "page": "plot_comparison", "title": "Compare EM-estimated mixture with a non-optimized reference model", "topics": [ "plot_comparison" ] }, { "page": "plot_distributions", "title": "Plot histogram with normal and stable PDF overlays", "topics": [ "plot_distributions" ] }, { "page": "plot_effective_reproduction_number", "title": "Plot effective reproduction number (Re) over time", "topics": [ "plot_effective_reproduction_number" ] }, { "page": "plot_final_mixture_fit", "title": "Plot final fitted mixture of alpha-stable distributions", "topics": [ "plot_final_mixture_fit" ] }, { "page": "plot_fit_vs_true", "title": "Plot true vs estimated mixture density", "topics": [ "plot_fit_vs_true" ] }, { "page": "plot_fit_vs_true_methods", "title": "Compare estimated mixture densities from two methods against the true density", "topics": [ "plot_fit_vs_true_methods" ] }, { "page": "plot_method_comparison", "title": "Plot RMSE and Log-Likelihood comparison across methods", "topics": [ "plot_method_comparison" ] }, { "page": "plot_mixture", "title": "Plot mixture of two alpha-stable distributions", "topics": [ "plot_mixture" ] }, { "page": "plot_mixture_fit", "title": "Plot mixture fit with individual components", "topics": [ "plot_mixture_fit" ] }, { "page": "plot_real_mixture_fit", "title": "Plot fitted mixture on real dataset", "topics": [ "plot_real_mixture_fit" ] }, { "page": "plot_results", "title": "Plot posterior mixture density from MCMC samples", "topics": [ "plot_results" ] }, { "page": "plot_trace", "title": "Plot trace of a parameter across MCMC iterations", "topics": [ "plot_trace" ] }, { "page": "plot_vs_normal_stable", "title": "Plot comparison between normal and stable distributions", "topics": [ "plot_vs_normal_stable" ] }, { "page": "qcv_stat", "title": "QCV statistic for tail heaviness", "topics": [ "qcv_stat" ] }, { "page": "r_stable_pdf", "title": "Robust stable PDF computation", "topics": [ "r_stable_pdf" ] }, { "page": "Re", "title": "Real part of the ECF integral", "topics": [ "Re" ] }, { "page": "recursive_weight", "title": "Recursive weight function", "topics": [ "recursive_weight" ] }, { "page": "robust_ecf_regression", "title": "Estimate stable parameters using robust ECF regression", "topics": [ "robust_ecf_regression" ] }, { "page": "robust_mle_estimate", "title": "Robust MLE estimation with multiple starting points", "topics": [ "robust_mle_estimate" ] }, { "page": "rstable", "title": "Generate random samples from stable distribution", "topics": [ "rstable" ] }, { "page": "RT", "title": "Compute effective reproduction number Rt", "topics": [ "RT" ] }, { "page": "run_all_estimations", "title": "Run all EM-based estimations without Gibbs sampling (CRAN-safe)", "topics": [ "run_all_estimations" ] }, { "page": "run_estimations_with_gibbs", "title": "Run all EM-based estimations with Gibbs sampling (CRAN-safe)", "topics": [ "run_estimations_with_gibbs" ] }, { "page": "safe_integrate", "title": "Safe integration wrapper with multiple fallback strategies", "topics": [ "safe_integrate" ] }, { "page": "simple_em_real", "title": "Simple 2-component EM using ECF initialization", "topics": [ "simple_em_real" ] }, { "page": "simulate_mixture", "title": "Simulate mixture data from alpha-stable components", "topics": [ "simulate_mixture" ] }, { "page": "sine_exp_ralpha", "title": "Sine exponential function", "topics": [ "sine_exp_ralpha" ] }, { "page": "sine_log_weighted_exp_ralpha", "title": "Sine-log-weighted exponential with r^(-alpha) term", "topics": [ "sine_log_weighted_exp_ralpha" ] }, { "page": "sine_r_weighted_exp_ralpha", "title": "Sine-r-weighted exponential function", "topics": [ "sine_r_weighted_exp_ralpha" ] }, { "page": "sine_weighted_exp_ralpha", "title": "Sine-weighted exponential with r^alpha term", "topics": [ "sine_weighted_exp_ralpha" ] }, { "page": "skew_kurtosis", "title": "Calculate skewness and kurtosis", "topics": [ "skew_kurtosis" ] }, { "page": "stable_fit_init", "title": "Initialize stable distribution parameters", "topics": [ "stable_fit_init" ] }, { "page": "TableS2_serial_interval_mean_", "title": "Example transmission pair data with mean serial interval", "topics": [ "TableS2_serial_interval_mean_" ] }, { "page": "test_normality", "title": "Test normality using multiple statistical tests", "topics": [ "test_normality" ] }, { "page": "unpack_params", "title": "Helper function to unpack parameters", "topics": [ "unpack_params" ] }, { "page": "validate_params", "title": "Validate and clip parameters for stable distribution", "topics": [ "validate_params" ] }, { "page": "wasserstein_distance_mixture", "title": "Wasserstein distance between two mixture distributions", "topics": [ "wasserstein_distance_mixture" ] } ], "_rundeps": [ "askpass", "base64enc", "bslib", "cachem", "class", "cli", "cpp11", "crosstalk", "curl", "data.table", "digest", "dplyr", "e1071", "evaluate", "farver", "fastmap", "fontawesome", "fs", "generics", "ggplot2", "glue", "gtable", "highr", "htmltools", "htmlwidgets", "httr", "isoband", "jquerylib", "jsonlite", "kernlab", "knitr", "labeling", "later", "lattice", "lazyeval", "libstable4u", "lifecycle", "magrittr", "MASS", "Matrix", "memoise", "mime", "mixtools", "nlme", "nortest", "openssl", "openxlsx", "otel", "pillar", "pkgconfig", "plotly", "promises", "proxy", "purrr", "R6", "rappdirs", "RColorBrewer", "Rcpp", "RcppGSL", "rlang", "rmarkdown", "S7", "sass", 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