{ "_id": "6ab8d5d999f7aa8c6aa3735d", "Package": "gkwdist", "Title": "Generalized Kumaraswamy Distribution Family", "Version": "1.1.7", "Authors@R": "c(person(given = \"José Evandeilton\",\nfamily = \"Lopes\",\nrole = c(\"aut\", \"cre\"),\nemail = \"evandeilton@gmail.com\",\ncomment = c(ORCID = \"0009-0007-5887-4084\")))", "Description": "Implements the five-parameter Generalized Kumaraswamy\n('gkw') distribution proposed by 'Carrasco, Ferrari and\nCordeiro (2010)' and its seven\nnested sub-families for modeling bounded continuous data on the\nunit interval (0,1). The 'gkw' distribution extends the\nKumaraswamy distribution described by Jones (2009)\n. Provides density,\ndistribution, quantile, and random generation functions, along\nwith analytical log-likelihood, gradient, and Hessian functions\nimplemented in 'C++' via 'RcppArmadillo' for maximum\ncomputational efficiency. Suitable for modeling proportions,\nrates, percentages, and indices exhibiting complex features\nsuch as asymmetry, or heavy tails and other shapes not\nadequately captured by standard distributions like simple Beta\nor Kumaraswamy.", "License": "MIT + file LICENSE", "URL": "https://github.com/evandeilton/gkwdist,\nhttps://evandeilton.github.io/gkwdist/", "BugReports": "https://github.com/evandeilton/gkwdist/issues", "Encoding": "UTF-8", "Language": "en-US", "Roxygen": "list(markdown = TRUE)", "Config/testthat/edition": "3", "NeedsCompilation": "yes", "VignetteBuilder": "knitr", "Config/roxygen2/version": "8.0.0", "Repository": "https://evandeilton.r-universe.dev", "Date/Publication": "2026-09-27 02:12:56 UTC", "RemoteUrl": "https://github.com/evandeilton/gkwdist", "RemoteRef": "HEAD", "RemoteSha": "0c18142fae193790486e0343d7f137b92c6bc640", "Packaged": { "Date": "2026-09-27 08:27:31 UTC", "User": "root" }, "Author": "José Evandeilton Lopes [aut, cre] (ORCID:\n)", "Maintainer": "José Evandeilton Lopes ", "_user": "evandeilton", "_type": "src", "_file": "gkwdist_1.1.7.tar.gz", "_fileid": "https://r2.ropensci.org/4c2078d1b8e0e40d546394e52037100126c6fb6447de37360537b27820d66f5c", "_filesize": 1890101, "_sha256": "4c2078d1b8e0e40d546394e52037100126c6fb6447de37360537b27820d66f5c", "_expires": "2027-01-05T08:37:43.000Z", "_created": "2026-09-27T08:27:31.000Z", "_published": "2026-09-27T08:37:44.906Z", "_jobs": [ { "job": 108583520317, "time": 212, "config": "linux-devel-arm64", "r": "4.7.0", "check": "OK", "artifact": "10927346660" }, { "job": 108583520354, "time": 233, "config": "linux-devel-x86_64", "r": "4.7.0", "check": "OK", "artifact": "10927900626" }, { "job": 108583520418, "time": 187, "config": "linux-release-arm64", "r": "4.6.1", "check": "OK", "artifact": "10927496334" }, { "job": 108583520324, "time": 204, "config": "linux-release-x86_64", "r": "4.6.1", "check": "OK", "artifact": "10927137267" }, { "job": 108583520321, "time": 224, "config": 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Distribution", "concept": [ "density functions", "kumaraswamy-kumaraswamy" ], "topics": [ "dkkw" ] }, { "page": "dkw", "title": "Density of the Kumaraswamy (Kw) Distribution", "concept": [ "density functions", "kumaraswamy" ], "topics": [ "dkw" ] }, { "page": "dmc", "title": "Density of the McDonald (Mc)/Beta Power Distribution", "concept": [ "density functions", "mcdonald" ], "topics": [ "dmc" ] }, { "page": "gkwgetstartvalues", "title": "Estimate Distribution Parameters Using Method of Moments", "topics": [ "gkwgetstartvalues" ] }, { "page": "grbeta", "title": "Gradient of the Negative Log-Likelihood for the Beta Distribution (gamma, delta+1 Parameterization)", "concept": [ "beta", "gradient functions" ], "topics": [ "grbeta" ] }, { "page": "grbkw", "title": "Gradient of the Negative Log-Likelihood for the BKw Distribution", "concept": [ "beta-kumaraswamy", "gradient functions" ], "topics": [ "grbkw" ] }, { "page": "grekw", "title": "Gradient of the Negative Log-Likelihood for the EKw Distribution", "concept": [ "exponentiated kumaraswamy", "gradient functions" ], "topics": [ "grekw" ] }, { "page": "grgkw", "title": "Gradient of the Negative Log-Likelihood for the GKw Distribution", "concept": [ "generalized kumaraswamy", "gradient functions" ], "topics": [ "grgkw" ] }, { "page": "grkkw", "title": "Gradient of the Negative Log-Likelihood for the KKw Distribution", "concept": [ "gradient functions", "kumaraswamy-kumaraswamy" ], "topics": [ "grkkw" ] }, { "page": "grkw", "title": "Gradient of the Negative Log-Likelihood for the Kumaraswamy (Kw) Distribution", "concept": [ "gradient functions", "kumaraswamy" ], "topics": [ "grkw" ] }, { "page": "grmc", "title": "Gradient of the Negative Log-Likelihood for the McDonald (Mc)/Beta Power Distribution", "concept": [ "gradient functions", "mcdonald" ], "topics": [ "grmc" ] }, { "page": "hsbeta", "title": "Hessian Matrix of the Negative Log-Likelihood for the Beta Distribution (gamma, delta+1 Parameterization)", "concept": [ "Hessian functions", "beta" ], "topics": [ "hsbeta" ] }, { "page": "hsbkw", "title": "Hessian Matrix of the Negative Log-Likelihood for the BKw Distribution", "concept": [ "Hessian functions", "beta-kumaraswamy" ], "topics": [ "hsbkw" ] }, { "page": "hsekw", "title": "Hessian Matrix of the Negative Log-Likelihood for the EKw Distribution", "concept": [ "Hessian functions", "exponentiated kumaraswamy" ], "topics": [ "hsekw" ] }, { "page": "hsgkw", "title": "Hessian Matrix of the Negative Log-Likelihood for the GKw Distribution", "concept": [ "Hessian functions", "generalized kumaraswamy" ], "topics": [ "hsgkw" ] }, { "page": "hskkw", "title": "Hessian Matrix of the Negative Log-Likelihood for the KKw Distribution", "concept": [ "Hessian functions", "kumaraswamy-kumaraswamy" ], "topics": [ "hskkw" ] }, { "page": "hskw", "title": "Hessian Matrix of the Negative Log-Likelihood for the Kw Distribution", "concept": [ "Hessian functions", "kumaraswamy" ], "topics": [ "hskw" ] }, { "page": "hsmc", "title": "Hessian Matrix of the Negative Log-Likelihood for the McDonald (Mc)/Beta Power Distribution", "concept": [ "Hessian functions", "mcdonald" ], "topics": [ "hsmc" ] }, { "page": "llbeta", "title": "Negative Log-Likelihood for the Beta Distribution (gamma, delta+1 Parameterization)", "concept": [ "beta", "log-likelihood functions" ], "topics": [ "llbeta" ] }, { "page": "llbkw", "title": "Negative Log-Likelihood for the Beta-Kumaraswamy (BKw) Distribution", "concept": [ "beta-kumaraswamy", "log-likelihood functions" ], "topics": [ "llbkw" ] }, { "page": "llekw", "title": "Negative Log-Likelihood for the Exponentiated Kumaraswamy (EKw) Distribution", "concept": [ "exponentiated kumaraswamy", "log-likelihood functions" ], "topics": [ "llekw" ] }, { "page": "llgkw", "title": "Negative Log-Likelihood for the Generalized Kumaraswamy Distribution", "concept": [ "generalized kumaraswamy", "log-likelihood functions" ], "topics": [ "llgkw" ] }, { "page": "llkkw", "title": "Negative Log-Likelihood for the KKw Distribution", "concept": [ "kumaraswamy-kumaraswamy", "log-likelihood functions" ], "topics": [ "llkkw" ] }, { "page": "llkw", "title": "Negative Log-Likelihood for the Kumaraswamy (Kw) Distribution", "concept": [ "kumaraswamy", "log-likelihood functions" ], "topics": [ "llkw" ] }, { "page": "llmc", "title": "Negative Log-Likelihood for the McDonald (Mc)/Beta Power Distribution", "concept": [ "log-likelihood functions", "mcdonald" ], "topics": [ "llmc" ] }, { "page": "pbeta_", "title": "Cumulative Distribution Function (CDF) of the Beta Distribution (gamma, delta+1 Parameterization)", "concept": [ "beta", "cumulative distribution functions" ], "topics": [ "pbeta_" ] }, { "page": "pbkw", "title": "Cumulative Distribution Function (CDF) of the Beta-Kumaraswamy (BKw) Distribution", "concept": [ "beta-kumaraswamy", "cumulative distribution functions" ], "topics": [ "pbkw" ] }, { "page": "pekw", "title": "Cumulative Distribution Function (CDF) of the EKw Distribution", "concept": [ "cumulative distribution functions", "exponentiated kumaraswamy" ], "topics": [ "pekw" ] }, { "page": "pgkw", "title": "Cumulative Distribution Function (CDF) of the Generalized Kumaraswamy Distribution", "concept": [ "cumulative distribution functions", "generalized kumaraswamy" ], "topics": [ "pgkw" ] }, { "page": "pkkw", "title": "Cumulative Distribution Function (CDF) of the KKw Distribution", "concept": [ "cumulative distribution functions", "kumaraswamy-kumaraswamy" ], "topics": [ "pkkw" ] }, { "page": "pkw", "title": "Cumulative Distribution Function (CDF) of the Kumaraswamy (Kw) Distribution", "concept": [ "cumulative distribution functions", "kumaraswamy" ], "topics": [ "pkw" ] }, { "page": "pmc", "title": "Cumulative Distribution Function (CDF) of the McDonald (Mc)/Beta Power Distribution", "concept": [ "cumulative distribution functions", "mcdonald" ], "topics": [ "pmc" ] }, { "page": "qbeta_", "title": "Quantile Function of the Beta Distribution (gamma, delta+1 Parameterization)", "concept": [ "beta", "quantile functions" ], "topics": [ "qbeta_" ] }, { "page": "qbkw", "title": "Quantile Function of the Beta-Kumaraswamy (BKw) Distribution", "concept": [ "beta-kumaraswamy", "quantile functions" ], "topics": [ "qbkw" ] }, { "page": "qekw", "title": "Quantile Function of the Exponentiated Kumaraswamy (EKw) Distribution", "concept": [ "exponentiated kumaraswamy", "quantile functions" ], "topics": [ "qekw" ] }, { "page": "qgkw", "title": "Quantile Function of the Generalized Kumaraswamy Distribution", "concept": [ "generalized kumaraswamy", "quantile functions" ], "topics": [ "qgkw" ] }, { "page": "qkkw", "title": "Quantile Function of the Kumaraswamy-Kumaraswamy (KKw) Distribution", "concept": [ "kumaraswamy-kumaraswamy", "quantile functions" ], "topics": [ "qkkw" ] }, { "page": "qkw", "title": "Quantile Function of the Kumaraswamy (Kw) Distribution", "concept": [ "kumaraswamy", "quantile functions" ], "topics": [ "qkw" ] }, { "page": "qmc", "title": "Quantile Function of the McDonald (Mc)/Beta Power Distribution", "concept": [ "mcdonald", "quantile functions" ], "topics": [ "qmc" ] }, { "page": "rbeta_", "title": "Random Number Generation for the Beta Distribution (gamma, delta+1 Parameterization)", "concept": [ "beta", "random generation functions" ], "topics": [ "rbeta_" ] }, { "page": "rbkw", "title": "Random Number Generation for the Beta-Kumaraswamy (BKw) Distribution", "concept": [ "beta-kumaraswamy", "random generation functions" ], "topics": [ "rbkw" ] }, { "page": "rekw", "title": "Random Number Generation for the Exponentiated Kumaraswamy (EKw) Distribution", "concept": [ "exponentiated kumaraswamy", "random generation functions" ], "topics": [ "rekw" ] }, { "page": "rgkw", "title": "Random Number Generation for the Generalized Kumaraswamy Distribution", "concept": [ "generalized kumaraswamy", "random generation functions" ], "topics": [ "rgkw" ] }, { "page": "rkkw", "title": "Random Number Generation for the KKw Distribution", "concept": [ "kumaraswamy-kumaraswamy", "random generation functions" ], "topics": [ "rkkw" ] }, { "page": "rkw", "title": "Random Number Generation for the Kumaraswamy (Kw) Distribution", "concept": [ "kumaraswamy", "random generation functions" ], "topics": [ "rkw" ] }, { "page": "rmc", "title": "Random Number Generation for the McDonald (Mc)/Beta Power Distribution", "concept": [ "mcdonald", "random generation functions" ], "topics": [ "rmc" ] } ], "_readme": "https://github.com/evandeilton/gkwdist/raw/HEAD/README.md", "_rundeps": [ "magrittr", "Rcpp", "RcppArmadillo" ], "_sysdeps": [ { "shlib": "libstdc++", "package": "libstdc++6", "source": "gcc", "version": "16-20260322-1ubuntu1", "name": "c++", "homepage": "http://gcc.gnu.org/", "description": "GNU Standard C++ Library v3" } ], "_vignettes": [ { "source": "gkwdist.Rmd", "filename": "gkwdist.html", "title": "Introduction to gkwdist: Generalized Kumaraswamy Distribution Family", "author": "José Evandeilton Lopes", "engine": "knitr::rmarkdown", "headings": [ "Introduction", "Key Features", "The Distribution Family", "Mathematical Foundation", "Nested Sub-families", "Basic Distribution Functions", "Density, CDF, Quantile, and Random Generation", "Visualization", "Comparing Distribution Shapes", "Flexibility Across Families", "Maximum Likelihood Estimation", "Basic MLE Workflow", "Inference Results", "Goodness-of-Fit Assessment", "Model Selection", "Comparing Nested Models", "Interpretation", "Advanced Topics", "Profile Likelihood", "Confidence Regions", "Performance Benchmarking", "Computational Efficiency", "Practical Applications", "Example: Modeling Proportions", "Recommendations", "When to Use Each Distribution", "Model Selection Workflow", "Conclusion", "Further Reading", "Session Information" ], "created": "2026-08-30 02:17:54", "modified": "2026-09-19 18:20:33", "commits": 3 }, { "source": "theory-gkwdist.Rmd", "filename": "theory-gkwdist.html", "title": "On the Statistical Properties and Computational Inference of the Generalized Kumaraswamy Distribution Family", "author": "José Evandeilton Lopes", "engine": "knitr::rmarkdown", "headings": [ "1. Introduction and Preliminaries", "1.1 Motivation and Background", "1.2 Mathematical Preliminaries", "2. The Generalized Kumaraswamy Distribution and Its Subfamilies", "2.1 Definition and Fundamental Properties", "2.2 The Hierarchical Structure", "2.2.1 Beta–Kumaraswamy distribution", "2.2.2 Kumaraswamy–Kumaraswamy distribution", "2.2.3 Exponentiated Kumaraswamy distribution", "2.2.4 McDonald distribution", "2.2.5 Kumaraswamy distribution", "2.2.6 Beta distribution", "3. Likelihood-Based Inference", "3.1 The Log-Likelihood Function", "3.2 Maximum Likelihood Estimation", "3.3 Likelihood Ratio Tests", "4. Analytical Derivatives and Information Matrix", "4.1 The Score Vector", "4.2 The Hessian and Observed Information Matrix", "4.2.1 Diagonal elements", "4.2.2 Off-diagonal elements", "4.3 Asymptotic Variance–Covariance Matrix", "5. Computational Aspects and Discussion", "5.1 Numerical Stability", "5.2 Optimization", "5.3 Gradient Accuracy", "5.4 Practical Recommendations", "5.5 Discussion", "References" ], "created": "2025-11-25 23:23:16", "modified": "2026-08-22 23:43:18", "commits": 2 } ], "_score": 5.653212513775344, "_indexed": true, "_nocasepkg": "gkwdist", "_universes": [ "evandeilton" ], "_binaries": [ { "r": "4.7.0", "os": "linux", "version": "1.1.7", "date": "2026-09-27T08:30:21.000Z", "distro": "resolute", "arch": "aarch64", "commit": "0c18142fae193790486e0343d7f137b92c6bc640", "fileid": "https://r2.ropensci.org/d17dd317a08cd75871bcd7ca383d5fe3705b072bd0c85a8594419fba58cf055d", "status": "success", "check": "OK", "buildurl": "https://github.com/r-universe/evandeilton/actions/runs/36306029823" }, { "r": "4.7.0", "os": "linux", "version": "1.1.7", "date": "2026-09-27T08:30:31.000Z", "distro": "resolute", "arch": "x86_64", "commit": "0c18142fae193790486e0343d7f137b92c6bc640", "fileid": 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