{ "_id": "6a18219dacfb0bcc41db2c18", "Package": "gkwdist", "Title": "Generalized Kumaraswamy Distribution Family", "Version": "1.1.4", "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", "RoxygenNote": "7.3.3", "Config/testthat/edition": "3", "NeedsCompilation": "yes", "VignetteBuilder": "knitr", "Packaged": { "Date": "2026-05-28 11:01:36 UTC", "User": "root" }, "Author": "José Evandeilton Lopes [aut, cre] (ORCID:\n)", "Maintainer": "José Evandeilton Lopes ", "Repository": "https://cran.r-universe.dev", "Date/Publication": "2026-05-28 08:56:06 UTC", "RemoteUrl": "https://github.com/cran/gkwdist", "RemoteRef": "HEAD", "RemoteSha": "e51d8f347d86f238f2405aaf167fa2ddb57ff8a4", "MD5sum": 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"rmarkdown", "role": "Suggests" }, { "package": "testthat", "version": ">= 3.0.0", "role": "Suggests" } ], "_owner": "cran", "_selfowned": false, "_usedby": 1, "_updates": [ { "week": "2025-46", "n": 1 }, { "week": "2025-48", "n": 1 }, { "week": "2026-02", "n": 1 }, { "week": "2026-21", "n": 1 }, { "week": "2026-22", "n": 1 } ], "_tags": [ { "name": "1.0.10", "date": "2025-11-13" }, { "name": "1.1.1", "date": "2025-11-27" }, { "name": "1.1.2", "date": "2026-01-08" }, { "name": "1.1.3", "date": "2026-05-21" }, { "name": "1.1.4", "date": "2026-05-28" } ], "_stars": 0, "_contributors": [ { "user": "evandeilton", "count": 5, "uuid": 9373260 } ], "_userbio": { "uuid": 6899542, "type": "organization", "name": "cran", "description": "Unofficial read-only mirror of all CRAN R packages" }, "_downloads": { "count": 586, "source": "https://cranlogs.r-pkg.org/downloads/total/last-month/gkwdist" }, "_devurl": "https://github.com/evandeilton/gkwdist", "_pkgdown": 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"llmc", "pbeta_", "pbkw", "pekw", "pgkw", "pkkw", "pkw", "pmc", "qbeta_", "qbkw", "qekw", "qgkw", "qkkw", "qkw", "qmc", "rbeta_", "rbkw", "rekw", "rgkw", "rkkw", "rkw", "rmc" ], "_help": [ { "page": "dbeta_", "title": "Density of the Beta Distribution (gamma, delta+1 Parameterization)", "topics": [ "dbeta_" ] }, { "page": "dbkw", "title": "Density of the Beta-Kumaraswamy (BKw) Distribution", "topics": [ "dbkw" ] }, { "page": "dekw", "title": "Density of the Exponentiated Kumaraswamy (EKw) Distribution", "topics": [ "dekw" ] }, { "page": "dgkw", "title": "Density of the Generalized Kumaraswamy Distribution", "topics": [ "dgkw" ] }, { "page": "dkkw", "title": "Density of the Kumaraswamy-Kumaraswamy (kkw) Distribution", "topics": [ "dkkw" ] }, { "page": "dkw", "title": "Density of the Kumaraswamy (Kw) Distribution", "topics": [ "dkw" ] }, { "page": "dmc", "title": "Density of the McDonald (Mc)/Beta Power Distribution Distribution", "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)", "topics": [ "grbeta" ] }, { "page": "grbkw", "title": "Gradient of the Negative Log-Likelihood for the BKw Distribution", "topics": [ "grbkw" ] }, { "page": "grekw", "title": "Gradient of the Negative Log-Likelihood for the EKw Distribution", "topics": [ "grekw" ] }, { "page": "grgkw", "title": "Gradient of the Negative Log-Likelihood for the GKw Distribution", "topics": [ "grgkw" ] }, { "page": "grkkw", "title": "Gradient of the Negative Log-Likelihood for the kkw Distribution", "topics": [ "grkkw" ] }, { "page": "grkw", "title": "Gradient of the Negative Log-Likelihood for the Kumaraswamy (Kw) Distribution", "topics": [ "grkw" ] }, { "page": "grmc", "title": "Gradient of the Negative Log-Likelihood for the McDonald (Mc)/Beta Power Distribution", "topics": [ "grmc" ] }, { "page": "hsbeta", "title": "Hessian Matrix of the Negative Log-Likelihood for the Beta Distribution (gamma, delta+1 Parameterization)", "topics": [ "hsbeta" ] }, { "page": "hsbkw", "title": "Hessian Matrix of the Negative Log-Likelihood for the BKw Distribution", "topics": [ "hsbkw" ] }, { "page": "hsekw", "title": "Hessian Matrix of the Negative Log-Likelihood for the EKw Distribution", "topics": [ "hsekw" ] }, { "page": "hsgkw", "title": "Hessian Matrix of the Negative Log-Likelihood for the GKw Distribution", "topics": [ "hsgkw" ] }, { "page": "hskkw", "title": "Hessian Matrix of the Negative Log-Likelihood for the kkw Distribution", "topics": [ "hskkw" ] }, { "page": "hskw", "title": "Hessian Matrix of the Negative Log-Likelihood for the Kw Distribution", "topics": [ "hskw" ] }, { "page": "hsmc", "title": "Hessian Matrix of the Negative Log-Likelihood for the McDonald (Mc)/Beta Power Distribution", "topics": [ "hsmc" ] }, { "page": "llbeta", "title": "Negative Log-Likelihood for the Beta Distribution (gamma, delta+1 Parameterization)", "topics": [ "llbeta" ] }, { "page": "llbkw", "title": "Negative Log-Likelihood for Beta-Kumaraswamy (BKw) Distribution", "topics": [ "llbkw" ] }, { "page": "llekw", "title": "Negative Log-Likelihood for the Exponentiated Kumaraswamy (EKw) Distribution", "topics": [ "llekw" ] }, { "page": "llgkw", "title": "Negative Log-Likelihood for the Generalized Kumaraswamy Distribution", "topics": [ "llgkw" ] }, { "page": "llkkw", "title": "Negative Log-Likelihood for the kkw Distribution", "topics": [ "llkkw" ] }, { "page": "llkw", "title": "Negative Log-Likelihood of the Kumaraswamy (Kw) Distribution", "topics": [ "llkw" ] }, { "page": "llmc", "title": "Negative Log-Likelihood for the McDonald (Mc)/Beta Power Distribution", "topics": [ "llmc" ] }, { "page": "pbeta_", "title": "CDF of the Beta Distribution (gamma, delta+1 Parameterization)", "topics": [ "pbeta_" ] }, { "page": "pbkw", "title": "Cumulative Distribution Function (CDF) of the Beta-Kumaraswamy (BKw) Distribution", "topics": [ "pbkw" ] }, { "page": "pekw", "title": "Cumulative Distribution Function (CDF) of the EKw Distribution", "topics": [ "pekw" ] }, { "page": "pgkw", "title": "Generalized Kumaraswamy Distribution CDF", "topics": [ "pgkw" ] }, { "page": "pkkw", "title": "Cumulative Distribution Function (CDF) of the kkw Distribution", "topics": [ "pkkw" ] }, { "page": "pkw", "title": "Cumulative Distribution Function (CDF) of the Kumaraswamy (Kw) Distribution", "topics": [ "pkw" ] }, { "page": "pmc", "title": "CDF of the McDonald (Mc)/Beta Power Distribution", "topics": [ "pmc" ] }, { "page": "qbeta_", "title": "Quantile Function of the Beta Distribution (gamma, delta+1 Parameterization)", "topics": [ "qbeta_" ] }, { "page": "qbkw", "title": "Quantile Function of the Beta-Kumaraswamy (BKw) Distribution", "topics": [ "qbkw" ] }, { "page": "qekw", "title": "Quantile Function of the Exponentiated Kumaraswamy (EKw) Distribution", "topics": [ "qekw" ] }, { "page": "qgkw", "title": "Generalized Kumaraswamy Distribution Quantile Function", "topics": [ "qgkw" ] }, { "page": "qkkw", "title": "Quantile Function of the Kumaraswamy-Kumaraswamy (kkw) Distribution", "topics": [ "qkkw" ] }, { "page": "qkw", "title": "Quantile Function of the Kumaraswamy (Kw) Distribution", "topics": [ "qkw" ] }, { "page": "qmc", "title": "Quantile Function of the McDonald (Mc)/Beta Power Distribution", "topics": [ "qmc" ] }, { "page": "rbeta_", "title": "Random Generation for the Beta Distribution (gamma, delta+1 Parameterization)", "topics": [ "rbeta_" ] }, { "page": "rbkw", "title": "Random Number Generation for the Beta-Kumaraswamy (BKw) Distribution", "topics": [ "rbkw" ] }, { "page": "rekw", "title": "Random Number Generation for the Exponentiated Kumaraswamy (EKw) Distribution", "topics": [ "rekw" ] }, { "page": "rgkw", "title": "Generalized Kumaraswamy Distribution Random Generation", "topics": [ "rgkw" ] }, { "page": "rkkw", "title": "Random Number Generation for the kkw Distribution", "topics": [ "rkkw" ] }, { "page": "rkw", "title": "Random Number Generation for the Kumaraswamy (Kw) Distribution", "topics": [ "rkw" ] }, { "page": "rmc", "title": "Random Number Generation for the McDonald (Mc)/Beta Power Distribution", "topics": [ "rmc" ] } ], "_readme": "https://github.com/cran/gkwdist/raw/HEAD/README.md", "_rundeps": [ "magrittr", "numDeriv", "Rcpp", "RcppArmadillo" ], "_sysdeps": [ { "shlib": "libblas", "package": "libopenblas0-pthread", "source": "openblas", "version": "0.3.26+ds-1ubuntu0.1", "name": "openblas", "homepage": "https://www.openblas.net/", "description": "Optimized BLAS (linear algebra) library (shared lib, pthread)" }, { "shlib": "libstdc++", "package": "libstdc++6", "source": "gcc", "version": "14.2.0-4ubuntu2~24.04.1", "name": "c++", "homepage": "http://gcc.gnu.org/", "description": "GNU Standard C++ Library v3" }, { "shlib": "libgomp", "package": "libgomp1", "source": 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Proportions", "Recommendations", "When to Use Each Distribution", "Model Selection Workflow", "Conclusion", "Further Reading", "Session Information" ], "created": "2025-11-13 19:28:05", "modified": "2025-11-27 06:10:23", "commits": 2 }, { "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 Subfamily", "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", "For (a<0), define[\\text{log1mexp}(a)", "5.2 Optimization", "5.3 Gradient Accuracy", "5.4 Practical Recommendations", "5.5 Discussion", "References" ], "created": "2025-11-27 06:10:23", "modified": "2025-11-27 06:10:23", "commits": 1 } ], "_score": 4.556302500767288, "_indexed": false, "_nocasepkg": "gkwdist", "_universes": [ "cran" ], "_indexurl": "https://evandeilton.r-universe.dev/gkwdist", "_previous": "1.1.3", "_binaries": [ { "r": "4.7.0", "os": "linux", "version": "1.1.4", "date": "2026-05-28T11:04:42.000Z", "distro": "noble", "arch": "aarch64", "commit": "e51d8f347d86f238f2405aaf167fa2ddb57ff8a4", "fileid": "eee81c298a9a8ff8145981e38bdea45a65c763a694cdea6828badb34d4af7209", "status": "success", "check": "OK", "buildurl": "https://github.com/r-universe/cran/actions/runs/26570562519" }, { "r": "4.7.0", "os": "linux", "version": "1.1.4", "date": "2026-05-28T11:04:36.000Z", "distro": "noble", "arch": "x86_64", "commit": "e51d8f347d86f238f2405aaf167fa2ddb57ff8a4", "fileid": "3f7f37cc6337e3239794f1b09f16a6640d915029d398d7eb1effd189aea9222a", "status": "success", "check": "OK", "buildurl": "https://github.com/r-universe/cran/actions/runs/26570562519" }, { "r": "4.6.0", "os": "linux", "version": "1.1.4", "date": "2026-05-28T11:04:36.000Z", "distro": "noble", "arch": "aarch64", "commit": "e51d8f347d86f238f2405aaf167fa2ddb57ff8a4", "fileid": "61f4248058ae332a50748209bfc71a0dfc5dbbf2d3c975bcc0ecca242ecd7620", "status": "success", "check": "OK", "buildurl": "https://github.com/r-universe/cran/actions/runs/26570562519" }, { "r": "4.6.0", "os": "linux", "version": "1.1.4", "date": "2026-05-28T11:04:37.000Z", "distro": "noble", "arch": "x86_64", "commit": "e51d8f347d86f238f2405aaf167fa2ddb57ff8a4", "fileid": "7e53c52dcdf4e2c5856a759d75928ad8703d4827e6f295c25b1fb92ad885d362", "status": "success", "check": "OK", "buildurl": "https://github.com/r-universe/cran/actions/runs/26570562519" }, { "r": "4.6.0", "os": "wasm", "version": "1.1.4", "date": "2026-05-28T11:04:43.000Z", "arch": "emscripten", "commit": "e51d8f347d86f238f2405aaf167fa2ddb57ff8a4", "fileid": "2a346de89c7ee3d283a5f732daee213dc2d59a51a3414f200aad32a176ddba50", "status": "success", "buildurl": "https://github.com/r-universe/cran/actions/runs/26570562519" } ] }