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  "Title": "Probabilistic Models to Analyze and Gaussianize Heavy-Tailed,\nSkewed Data",
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  "Description": "Lambert W x F distributions are a generalized framework to\nanalyze skewed, heavy-tailed data. It is based on an\ninput/output system, where the output random variable (RV) Y is\na non-linearly transformed version of an input RV X ~ F with\nsimilar properties as X, but slightly skewed (heavy-tailed).\nThe transformed RV Y has a Lambert W x F distribution. This\npackage contains functions to model and analyze skewed,\nheavy-tailed data the Lambert Way: simulate random samples,\nestimate parameters, compute quantiles, and plot/ print results\nnicely. The most useful function is 'Gaussianize', which works\nsimilarly to 'scale', but actually makes the data Gaussian. A\ndo-it-yourself toolkit allows users to define their own Lambert\nW x 'MyFavoriteDistribution' and use it in their analysis right\naway.",
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  "Repository": "https://gmgeorg.r-universe.dev",
  "Date/Publication": "2025-08-21 15:30:16 UTC",
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    "bounds_theta",
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    "check_tau",
    "check_theta",
    "complete_tau",
    "complete_theta",
    "create_LambertW_input",
    "create_LambertW_output",
    "d1W_1",
    "delta_01",
    "delta_GMM",
    "delta_Taylor",
    "deriv_log_W",
    "deriv_W",
    "deriv_W_delta",
    "deriv_W_delta_alpha",
    "deriv_W_gamma",
    "deriv_xexp",
    "dLambertW",
    "dU",
    "estimate_beta",
    "flatten_theta",
    "G_2delta_2alpha",
    "G_delta",
    "G_delta_alpha",
    "gamma_01",
    "gamma_GMM",
    "gamma_Taylor",
    "Gaussianize",
    "get_beta_names",
    "get_distname_family",
    "get_distnames",
    "get_gamma_bounds",
    "get_initial_tau",
    "get_initial_theta",
    "get_input",
    "get_output",
    "get_support",
    "get_theta_bounds",
    "get.input",
    "H",
    "H_gamma",
    "IGMM",
    "ks_test_t",
    "kurtosis",
    "log_deriv_W",
    "log_W",
    "loglik_input",
    "loglik_LambertW",
    "loglik_penalty",
    "lp_norm",
    "medcouple_estimator",
    "mLambertW",
    "MLE_LambertW",
    "normalize_by_tau",
    "normfit",
    "p_1",
    "p_m1",
    "params2theta",
    "pLambertW",
    "pU",
    "qLambertW",
    "qqLambertW",
    "qU",
    "rLambertW",
    "rU",
    "skewness",
    "skewness_test",
    "starting_theta",
    "support",
    "tau2theta",
    "tau2type",
    "test_norm",
    "test_normality",
    "test_symmetry",
    "theta2params",
    "theta2tau",
    "theta2unbounded",
    "unflatten_theta",
    "vec.norm",
    "W",
    "W_1",
    "W_2delta",
    "W_2delta_2alpha",
    "W_delta",
    "W_delta_alpha",
    "W_gamma",
    "W_gamma_1",
    "xexp"
  ],
  "_datasets": [
    {
      "name": "AA",
      "title": "Datasets",
      "object": "AA",
      "file": "AA.rda",
      "class": [
        "data.frame"
      ],
      "fields": [
        "rcc",
        "wcc",
        "hc",
        "hg",
        "ferr",
        "bmi",
        "ssf",
        "pcBfat",
        "lbm",
        "ht",
        "wt",
        "sex",
        "sport"
      ],
      "rows": 202,
      "table": true,
      "tojson": true
    },
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      "title": "Datasets",
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      "file": "SolarFlares.rda",
      "class": [
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      ],
      "fields": [],
      "table": false,
      "tojson": true
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  "_help": [
    {
      "page": "analyze_convergence",
      "title": "Analyze convergence of Lambert W estimators",
      "topics": [
        "analyze_convergence",
        "plot.convergence_LambertW_fit",
        "summary.convergence_LambertW_fit"
      ]
    },
    {
      "page": "beta-utils",
      "title": "Utilities for parameter vector beta of the input distribution",
      "topics": [
        "beta-utils",
        "beta2tau",
        "check_beta",
        "estimate_beta",
        "get_beta_names"
      ]
    },
    {
      "page": "bootstrap",
      "title": "Bootstrap Lambert W x F estimates",
      "topics": [
        "bootstrap",
        "bootstrap.LambertW_fit"
      ]
    },
    {
      "page": "common-arguments",
      "title": "Common arguments for several functions",
      "topics": [
        "common-arguments"
      ]
    },
    {
      "page": "datasets",
      "title": "Datasets",
      "topics": [
        "AA",
        "datasets",
        "SolarFlares"
      ]
    },
    {
      "page": "delta_01",
      "title": "Input parameters to get zero mean, unit variance output given delta",
      "topics": [
        "delta_01"
      ]
    },
    {
      "page": "delta_GMM",
      "title": "Estimate delta",
      "topics": [
        "delta_GMM"
      ]
    },
    {
      "page": "delta_Taylor",
      "title": "Estimate of delta by Taylor approximation",
      "topics": [
        "delta_Taylor"
      ]
    },
    {
      "page": "deprecated-functions",
      "title": "List of deprecated functions",
      "topics": [
        "beta_names",
        "bounds_theta",
        "d1W_1",
        "deprecated-functions",
        "H",
        "normfit",
        "params2theta",
        "p_1",
        "skewness_test",
        "starting_theta",
        "support",
        "theta2params",
        "vec.norm",
        "W_1",
        "W_gamma_1"
      ]
    },
    {
      "page": "distname-utils",
      "title": "Utilities for distributions supported in this package",
      "topics": [
        "check_distname",
        "distname-utils",
        "get_distnames",
        "get_distname_family"
      ]
    },
    {
      "page": "G_delta_alpha",
      "title": "Heavy tail transformation for Lambert W random variables",
      "topics": [
        "G_2delta_2alpha",
        "G_delta",
        "G_delta_alpha"
      ]
    },
    {
      "page": "gamma_01",
      "title": "Input parameters to get a zero mean, unit variance output for a given gamma",
      "topics": [
        "gamma_01"
      ]
    },
    {
      "page": "gamma_GMM",
      "title": "Estimate gamma",
      "topics": [
        "gamma_GMM"
      ]
    },
    {
      "page": "gamma_Taylor",
      "title": "Estimate gamma by Taylor approximation",
      "topics": [
        "gamma_Taylor"
      ]
    },
    {
      "page": "Gaussianize",
      "title": "Gaussianize matrix-like objects",
      "topics": [
        "Gaussianize"
      ]
    },
    {
      "page": "get_gamma_bounds",
      "title": "Get bounds for gamma",
      "topics": [
        "get_gamma_bounds"
      ]
    },
    {
      "page": "get_input",
      "title": "Back-transform Y to X",
      "topics": [
        "get.input",
        "get_input"
      ]
    },
    {
      "page": "get_output",
      "title": "Transform input X to output Y",
      "topics": [
        "get_output"
      ]
    },
    {
      "page": "get_support",
      "title": "Computes support for skewed Lambert W x F distributions",
      "topics": [
        "get_support"
      ]
    },
    {
      "page": "H_gamma",
      "title": "H transformation with gamma",
      "topics": [
        "H_gamma"
      ]
    },
    {
      "page": "IGMM",
      "title": "Iterative Generalized Method of Moments - IGMM",
      "topics": [
        "IGMM"
      ]
    },
    {
      "page": "ks_test_t",
      "title": "One-sample Kolmogorov-Smirnov test for student-t distribution",
      "topics": [
        "ks_test_t"
      ]
    },
    {
      "page": "estimate-moments",
      "title": "Skewness and kurtosis",
      "topics": [
        "kurtosis",
        "skewness"
      ]
    },
    {
      "page": "LambertW_fit-methods",
      "title": "Methods for Lambert W\\times F estimates",
      "topics": [
        "LambertW_fit-methods",
        "plot.LambertW_fit",
        "print.LambertW_fit",
        "print.summary.LambertW_fit",
        "summary.LambertW_fit"
      ]
    },
    {
      "page": "LambertW_input_output-methods",
      "title": "Methods for Lambert W input and output objects",
      "topics": [
        "LambertW_input_output-methods",
        "plot.LambertW_input",
        "plot.LambertW_output",
        "print.LambertW_input",
        "print.LambertW_output"
      ]
    },
    {
      "page": "LambertW-toolkit",
      "title": "Do-it-yourself toolkit for Lambert W \\times F distribution",
      "topics": [
        "create_LambertW_input",
        "create_LambertW_output",
        "LambertW-toolkit"
      ]
    },
    {
      "page": "LambertW-utils",
      "title": "Utilities for Lambert W \\times F Random Variables",
      "topics": [
        "dLambertW",
        "LambertW-utils",
        "mLambertW",
        "pLambertW",
        "qLambertW",
        "qqLambertW",
        "rLambertW"
      ]
    },
    {
      "page": "loglik-LambertW-utils",
      "title": "Log-Likelihood for Lambert W\\times F RVs",
      "topics": [
        "loglik-LambertW-utils",
        "loglik_input",
        "loglik_LambertW",
        "loglik_penalty"
      ]
    },
    {
      "page": "lp_norm",
      "title": "lp norm of a vector",
      "topics": [
        "lp_norm"
      ]
    },
    {
      "page": "medcouple_estimator",
      "title": "MedCouple Estimator",
      "topics": [
        "medcouple_estimator"
      ]
    },
    {
      "page": "MLE_LambertW",
      "title": "Maximum Likelihood Estimation for Lambert W \\times F distributions",
      "topics": [
        "MLE_LambertW"
      ]
    },
    {
      "page": "p_m1",
      "title": "Non-principal branch probability",
      "topics": [
        "p_m1"
      ]
    },
    {
      "page": "tau-utils",
      "title": "Utilities for transformation vector tau",
      "topics": [
        "check_tau",
        "complete_tau",
        "get_initial_tau",
        "normalize_by_tau",
        "tau-utils",
        "tau2theta",
        "tau2type"
      ]
    },
    {
      "page": "test_normality",
      "title": "Visual and statistical Gaussianity check",
      "topics": [
        "test_norm",
        "test_normality"
      ]
    },
    {
      "page": "test_symmetry",
      "title": "Test symmetry based on Lambert W heavy tail(s)",
      "topics": [
        "test_symmetry"
      ]
    },
    {
      "page": "theta-utils",
      "title": "Utilities for the parameter vector of Lambert W\\times F distributions",
      "topics": [
        "check_theta",
        "complete_theta",
        "flatten_theta",
        "get_initial_theta",
        "get_theta_bounds",
        "theta-utils",
        "theta2tau",
        "theta2unbounded",
        "unflatten_theta"
      ]
    },
    {
      "page": "U-utils",
      "title": "Zero-mean, unit-variance version of standard distributions",
      "topics": [
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