{ "_id": "6a16ce4aacfb0bcc41d8a477", "Package": "Pareto", "Type": "Package", "Title": "The Pareto, Piecewise Pareto and Generalized Pareto Distribution", "Version": "2.4.5", "Authors@R": "person(\"Ulrich\", \"Riegel\", email = \"ulrich.riegel@gmx.de\", role = c(\"aut\", \"cre\"))", "Description": "Utilities for the Pareto, piecewise Pareto and generalized\nPareto distribution that are useful for reinsurance pricing. In\nparticular, the package provides a non-trivial algorithm that\ncan be used to match the expected losses of a tower of\nreinsurance layers with a layer-independent collective risk\nmodel. The theoretical background of the matching algorithm and\nmost other methods are described in Ulrich Riegel (2018)\n.", "License": "GPL (>= 2)", "Encoding": "UTF-8", "LazyData": "true", "RoxygenNote": "7.2.3", "VignetteBuilder": "knitr", "URL": "https://github.com/ulrichriegel/Pareto#pareto", "Language": "en-US", "Repository": "https://ulrichriegel.r-universe.dev", "Date/Publication": "2023-04-17 20:17:38 UTC", "RemoteUrl": "https://github.com/ulrichriegel/pareto", "RemoteRef": "HEAD", "RemoteSha": "4da101e02872456798ee8039e04f5a992de5bb98", "NeedsCompilation": "no", "Packaged": { "Date": "2026-05-27 10:55:32 UTC", "User": "root" }, "Author": "Ulrich Riegel [aut, cre]", "Maintainer": "Ulrich Riegel ", "MD5sum": "07f7708ba4eaa81a2c696a2cc7b15380", "_user": "ulrichriegel", "_type": "src", "_file": "Pareto_2.4.5.tar.gz", "_fileid": "1fb3532e3d58edbcbf4fb631226839ac2877cc49e3f7b2b67d6eff78a1a5b024", "_filesize": 530230, "_sha256": "1fb3532e3d58edbcbf4fb631226839ac2877cc49e3f7b2b67d6eff78a1a5b024", "_created": "2026-05-27T10:55:32.000Z", "_published": "2026-05-27T10:58:18.226Z", "_distro": "noble", "_jobs": [ { "job": 78061660633, "time": 127, "config": "linux-devel-x86_64", "r": "4.7.0", "check": "OK", "artifact": "7238597176" }, { "job": 78061660630, "time": 123, "config": "linux-release-x86_64", "r": "4.6.0", "check": "OK", "artifact": "7238596084" }, { "job": 78061660664, "time": 72, "config": "macos-oldrel-arm64", "r": "4.5.3", "check": "OK", "artifact": "7238580072" }, { "job": 78061660635, "time": 104, "config": "macos-release-arm64", "r": "4.6.0", "check": "OK", "artifact": "7238589705" }, { "job": 78061229100, "time": 161, "config": "source", "r": "4.6.0", "check": "OK", "artifact": "7238555782" }, { "job": 78061660637, "time": 91, "config": "wasm-release", "r": "4.6.0", "check": "OK", "artifact": "7238586017" }, { "job": 78061660692, "time": 103, "config": "windows-devel", "r": "4.7.0", "check": "OK", "artifact": "7238589119" }, { "job": 78061660684, "time": 103, "config": "windows-oldrel", "r": "4.5.3", "check": "OK", "artifact": "7238589620" }, { "job": 78061660853, "time": 122, "config": "windows-release", "r": "4.6.0", "check": "OK", "artifact": "7238595909" } ], "_buildurl": "https://github.com/r-universe/ulrichriegel/actions/runs/26506805164", "_status": "success", "_host": "GitHub-Actions", "_upstream": "https://github.com/ulrichriegel/pareto", "_commit": { "id": "4da101e02872456798ee8039e04f5a992de5bb98", "author": "ulrichriegel ", "committer": "ulrichriegel ", "message": "Create CRAN-SUBMISSION\n", "time": 1681762658 }, "_maintainer": { "name": "Ulrich Riegel", "email": "ulrich.riegel@gmx.de", "login": "ulrichriegel", "description": "", "uuid": 29739901 }, "_registered": true, "_dependencies": [ { "package": "R", "version": ">= 2.10", "role": "Depends" }, { "package": "testthat", "role": "Suggests" }, { "package": "knitr", "role": "Suggests" }, { "package": "rmarkdown", "role": "Suggests" }, { "package": "lpSolve", "role": "Suggests" } ], "_owner": "ulrichriegel", "_selfowned": true, "_usedby": 1, "_updates": [], "_tags": [], "_stars": 11, "_contributors": [ { "user": "ulrichriegel", "count": 194, "uuid": 29739901 } ], "_userbio": { "uuid": 29739901, "type": "user", "name": "Ulrich Riegel" }, "_downloads": { "count": 874, "source": "https://cranlogs.r-pkg.org/downloads/total/last-month/Pareto" }, "_mentions": 4, "_devurl": "https://github.com/ulrichriegel/pareto", "_searchresults": 211, "_rbuild": "4.6.0", "_assets": [ "extra/citation.cff", "extra/citation.html", "extra/citation.json", "extra/citation.txt", "extra/contents.json", "extra/NEWS.html", "extra/NEWS.txt", "extra/Pareto.html", "extra/readme.html", "extra/readme.md", "manual.pdf" ], "_homeurl": "https://github.com/ulrichriegel/pareto", "_realowner": "ulrichriegel", "_cranurl": true, "_releases": [ { "version": "1.1.0", "date": "2019-12-17" }, { "version": "1.1.3", "date": "2020-02-14" }, { "version": "1.1.5", "date": "2020-04-03" }, { "version": "2.0.0", "date": "2020-05-02" }, { "version": "2.1.0", "date": "2020-07-09" }, { "version": "2.2.0", "date": "2020-08-03" }, { "version": "2.2.1", "date": "2020-09-11" }, { "version": "2.2.2", "date": "2021-01-28" }, { "version": "2.3.0", "date": "2021-02-07" }, { "version": "2.4.0", "date": "2021-02-18" }, { "version": "2.4.2", "date": "2021-03-03" }, { "version": "2.4.4", "date": "2023-04-08" }, { "version": "2.4.5", "date": "2023-04-18" } ], "_exports": [ "dGenPareto", "dPareto", "dPiecewisePareto", "Excess_Frequency", "Fit_PML_Curve", "Fit_References", "GenPareto_Layer_Mean", "GenPareto_Layer_SM", "GenPareto_Layer_Var", "GenPareto_ML_Estimator_Alpha", "is.PGP_Model", "is.PPP_Model", "is.valid.PGP_Model", "is.valid.PPP_Model", "Layer_Mean", "Layer_Sd", "Layer_Var", "Local_Pareto_Alpha", "Pareto_CDF", "Pareto_Extrapolation", "Pareto_Find_Alpha_btw_FQ_Layer", "Pareto_Find_Alpha_btw_FQs", "Pareto_Find_Alpha_btw_Layers", "Pareto_Layer_Mean", "Pareto_Layer_SM", "Pareto_Layer_Var", "Pareto_ML_Estimator_Alpha", "Pareto_PDF", "pGenPareto", "PGP_Model", "PiecewisePareto_CDF", "PiecewisePareto_Layer_Mean", "PiecewisePareto_Layer_SM", "PiecewisePareto_Layer_Var", "PiecewisePareto_Match_Layer_Losses", "PiecewisePareto_ML_Estimator_Alpha", "PiecewisePareto_PDF", "pPareto", "pPiecewisePareto", "PPP_Model", "PPP_Model_Excess_Frequency", "PPP_Model_Exp_Layer_Loss", "PPP_Model_Layer_Sd", "PPP_Model_Layer_Var", "PPP_Model_Simulate", "qGenPareto", "qPareto", "qPiecewisePareto", "rGenPareto", "rPareto", "rPiecewisePareto", "Simulate_Losses" ], "_datasets": [ { "name": "Example1_AP", "title": "Example data: Attachment Points", "object": "Example1_AP", "class": [ "numeric" ], "fields": [], "table": false, "tojson": true }, { "name": "Example1_EL", "title": "Example data: Expected Losses", "object": "Example1_EL", "class": [ "numeric" ], "fields": [], "table": false, "tojson": true } ], "_help": [ { "page": "dGenPareto", "title": "Density of the generalized Pareto Distribution", "topics": [ "dGenPareto" ] }, { "page": "dPareto", "title": "Density of the Pareto Distribution", "topics": [ "dPareto" ] }, { "page": "dPiecewisePareto", "title": "Density of the Piecewise Pareto Distribution", "topics": [ "dPiecewisePareto" ] }, { "page": "Example1_AP", "title": "Example data: Attachment Points", "topics": [ "Example1_AP" ] }, { "page": "Example1_EL", "title": "Example data: Expected Losses", "topics": [ "Example1_EL" ] }, { "page": "Excess_Frequency", "title": "Expected Frequency in Excess of a Threshold", "topics": [ "Excess_Frequency" ] }, { "page": "Excess_Frequency.PGP_Model", "title": "Expected Frequency in Excess of a Threshold", "topics": [ "Excess_Frequency.PGP_Model" ] }, { "page": "Excess_Frequency.PPP_Model", "title": "Expected Frequency in Excess of a Threshold", "topics": [ "Excess_Frequency.PPP_Model" ] }, { "page": "Fit_PML_Curve", "title": "Fits a Collective Model to a PML Curve", "topics": [ "Fit_PML_Curve" ] }, { "page": "Fit_References", "title": "Fit a Collective Model to a Wishlist of References", "topics": [ "Fit_References" ] }, { "page": "GenPareto_Layer_Mean", "title": "Layer Mean of the generalized Pareto Distribution", "topics": [ "GenPareto_Layer_Mean" ] }, { "page": "GenPareto_Layer_SM", "title": "Second Layer Moment of the Generalized Pareto Distribution", "topics": [ "GenPareto_Layer_SM" ] }, { "page": "GenPareto_Layer_Var", "title": "Layer Variance of the Generalized Pareto Distribution", "topics": [ "GenPareto_Layer_Var" ] }, { "page": "GenPareto_ML_Estimator_Alpha", "title": "Maximum Likelihood Estimation of the Pareto Alphas of a Generalized Pareto Distribution", "topics": [ "GenPareto_ML_Estimator_Alpha" ] }, { "page": "is.PGP_Model", "title": "Check if an object is a PGP_Model", "topics": [ "is.PGP_Model" ] }, { "page": "is.PPP_Model", "title": "Check if an object is a PPP_Model", "topics": [ "is.PPP_Model" ] }, { "page": "is.valid.PGP_Model", "title": "Check if an object is a valid PGP_Model", "topics": [ "is.valid.PGP_Model" ] }, { "page": "is.valid.PPP_Model", "title": "Check if an object is a valid PPP_Model", "topics": [ "is.valid.PPP_Model" ] }, { "page": "Layer_Mean", "title": "Expected Loss of a Reinsurance Layer", "topics": [ "Layer_Mean" ] }, { "page": "Layer_Mean.PGP_Model", "title": "Expected Loss of a Reinsurance Layer", "topics": [ "Layer_Mean.PGP_Model" ] }, { "page": "Layer_Mean.PPP_Model", "title": "Expected Loss of a Reinsurance Layer", "topics": [ "Layer_Mean.PPP_Model" ] }, { "page": "Layer_Sd", "title": "Standard Deviation of a Reinsurance Layer", "topics": [ "Layer_Sd" ] }, { "page": "Layer_Sd.PGP_Model", "title": "Standard Deviation of a Reinsurance Layer", "topics": [ "Layer_Sd.PGP_Model" ] }, { "page": "Layer_Sd.PPP_Model", "title": "Standard Deviation of a Reinsurance Layer", "topics": [ "Layer_Sd.PPP_Model" ] }, { "page": "Layer_Var", "title": "Variance of a Reinsurance Layer", "topics": [ "Layer_Var" ] }, { "page": "Layer_Var.PGP_Model", "title": "Variance of a Reinsurance Layer", "topics": [ "Layer_Var.PGP_Model" ] }, { "page": "Layer_Var.PPP_Model", "title": "Variance of a Reinsurance Layer", "topics": [ "Layer_Var.PPP_Model" ] }, { "page": "Local_Pareto_Alpha", "title": "Local Pareto Alpha", "topics": [ "Local_Pareto_Alpha" ] }, { "page": "Pareto_CDF", "title": "Distribution Function of the Pareto Distribution", "topics": [ "Pareto_CDF" ] }, { "page": "Pareto_Extrapolation", "title": "Pareto Extrapolation", "topics": [ "Pareto_Extrapolation" ] }, { "page": "Pareto_Find_Alpha_btw_FQ_Layer", "title": "Pareto Alpha Between a Frequency and a Layer", "topics": [ "Pareto_Find_Alpha_btw_FQ_Layer" ] }, { "page": "Pareto_Find_Alpha_btw_FQs", "title": "Pareto Alpha Between Two Frequencies", "topics": [ "Pareto_Find_Alpha_btw_FQs" ] }, { "page": "Pareto_Find_Alpha_btw_Layers", "title": "Pareto Alpha Between Two Layers", "topics": [ "Pareto_Find_Alpha_btw_Layers" ] }, { "page": "Pareto_Layer_Mean", "title": "Layer Mean of the Pareto Distribution", "topics": [ "Pareto_Layer_Mean" ] }, { "page": "Pareto_Layer_SM", "title": "Second Layer Moment of the Pareto Distribution", "topics": [ "Pareto_Layer_SM" ] }, { "page": "Pareto_Layer_Var", "title": "Layer Variance of the Pareto Distribution", "topics": [ "Pareto_Layer_Var" ] }, { "page": "Pareto_ML_Estimator_Alpha", "title": "Maximum Likelihood Estimation of the Alpha of a Pareto distribution", "topics": [ "Pareto_ML_Estimator_Alpha" ] }, { "page": "Pareto_PDF", "title": "Density of the Pareto Distribution", "topics": [ "Pareto_PDF" ] }, { "page": "pGenPareto", "title": "Distribution Function of the generalized Pareto Distribution", "topics": [ "pGenPareto" ] }, { "page": "PGP_Model", "title": "PGP_Model (Collective Panjer & Generalized Pareto Model) Object", "topics": [ "PGP_Model" ] }, { "page": "PiecewisePareto_CDF", "title": "Distribution Function of the Piecewise Pareto Distribution", "topics": [ "PiecewisePareto_CDF" ] }, { "page": "PiecewisePareto_Layer_Mean", "title": "Layer Mean of the Piecewise Pareto Distribution", "topics": [ "PiecewisePareto_Layer_Mean" ] }, { "page": "PiecewisePareto_Layer_SM", "title": "Second Layer Moment of the Piecewise Pareto Distribution", "topics": [ "PiecewisePareto_Layer_SM" ] }, { "page": "PiecewisePareto_Layer_Var", "title": "Layer Variance of the Piecewise Pareto Distribution", "topics": [ "PiecewisePareto_Layer_Var" ] }, { "page": "PiecewisePareto_Match_Layer_Losses", "title": "Match a Tower of Expected Layers Losses", "topics": [ "PiecewisePareto_Match_Layer_Losses" ] }, { "page": "PiecewisePareto_ML_Estimator_Alpha", "title": "Maximum Likelihood Estimation of the Alphas of the Piecewise Pareto Distribution", "topics": [ "PiecewisePareto_ML_Estimator_Alpha" ] }, { "page": "PiecewisePareto_PDF", "title": "Density of the Piecewise Pareto Distribution", "topics": [ "PiecewisePareto_PDF" ] }, { "page": "pPareto", "title": "Distribution Function of the Pareto Distribution", "topics": [ "pPareto" ] }, { "page": "pPiecewisePareto", "title": "Distribution Function of the Piecewise Pareto Distribution", "topics": [ "pPiecewisePareto" ] }, { "page": "PPP_Model", "title": "PPP_Model (Collective Panjer & Piecewise Pareto Model) Object", "topics": [ "PPP_Model" ] }, { "page": "PPP_Model_Excess_Frequency", "title": "Expected Frequency in Excess of a Threshold", "topics": [ "PPP_Model_Excess_Frequency" ] }, { "page": "PPP_Model_Exp_Layer_Loss", "title": "Expected Loss of a Reinsurance Layer", "topics": [ "PPP_Model_Exp_Layer_Loss" ] }, { "page": "PPP_Model_Layer_Sd", "title": "Standard Deviation of a Reinsurance Layer", "topics": [ "PPP_Model_Layer_Sd" ] }, { "page": "PPP_Model_Layer_Var", "title": "Variance of a Reinsurance Layer", "topics": [ "PPP_Model_Layer_Var" ] }, { "page": "PPP_Model_Simulate", "title": "Simulate Losses with a PPP_Model", "topics": [ "PPP_Model_Simulate" ] }, { "page": "print.PGP_Model", "title": "Print a PGP_Model Object (Collective Panjer & Generalized Pareto Model) Object", "topics": [ "print.PGP_Model" ] }, { "page": "print.PPP_Model", "title": "Print a PPP_Model Object (Collective Panjer & Piecewise Pareto Model) Object", "topics": [ "print.PPP_Model" ] }, { "page": "qGenPareto", "title": "Quantile Function of the generalized Pareto Distribution", "topics": [ "qGenPareto" ] }, { "page": "qPareto", "title": "Quantile Function of the Pareto Distribution", "topics": [ "qPareto" ] }, { "page": "qPiecewisePareto", "title": "Quantile Function of the Piecewise Pareto Distribution", "topics": [ "qPiecewisePareto" ] }, { "page": "rGenPareto", "title": "Simulation of the generalized Pareto Distribution", "topics": [ "rGenPareto" ] }, { "page": "rPareto", "title": "Simulation of the Pareto Distribution", "topics": [ "rPareto" ] }, { "page": "rPiecewisePareto", "title": "Simulation of the Piecewise Pareto Distribution", "topics": [ "rPiecewisePareto" ] }, { "page": "Simulate_Losses", "title": "Simulate Losses with a Collective Model", "topics": [ "Simulate_Losses" ] }, { "page": "Simulate_Losses.PGP_Model", "title": "Simulate Losses with a PGP_Model", "topics": [ "Simulate_Losses.PGP_Model" ] }, { "page": "Simulate_Losses.PPP_Model", "title": "Simulate Losses with a PPP_Model", "topics": [ "Simulate_Losses.PPP_Model" ] } ], "_readme": "https://github.com/ulrichriegel/pareto/raw/HEAD/README.md", "_rundeps": [], "_vignettes": [ { "source": "Pareto.Rmd", "filename": "Pareto.html", "title": "Pareto Package Vignette", "author": "Ulrich Riegel", "engine": "knitr::rmarkdown", "headings": [ "Introduction", "Pareto distribution", "Distribution function and density", "Simulation:", "Layer mean:", "Layer variance:", "Why is the Pareto distribution so popular?", "Pareto extrapolation", "Pareto alpha between two layers:", "Pareto alpha between a frequency and layer:", "Matching the expected losses of two layers:", "Frequency extrapolation and alpha between frequencies:", "Maximum likelihood estimation of the parameter alpha", "Truncation", "Piecewise Pareto distribution", "Distribution function", "Density", "Simulation", "Layer mean", "Layer variance", "Maximum likelihood estimation of the alphas", "Matching a tower of layer losses", "Matching reference information", "Interpolation of PML curves", "PPP_Models (Panjer & Piecewise Pareto Models)", "Expected Loss, Standard Deviation and Variance for Reinsurance Layers", "Expected Excess Frequency", "Simulation of Losses", "Generalized Pareto Distribution", "Maximum likelihood estimation of the alpha_ini and alpha_tail", "PGP_Models (Panjer & Generalized Pareto Models)", "Methods for PGP_Models", "References" ], "created": "2019-11-16 00:35:15", "modified": "2021-02-18 09:24:57", "commits": 18 } ], "_score": 7.143826390839561, "_indexed": true, "_nocasepkg": "pareto", "_universes": [ "ulrichriegel" ], "_binaries": [ { "r": "4.7.0", "os": "linux", "version": "2.4.5", "date": "2026-05-27T10:57:39.000Z", "distro": "noble", "commit": "4da101e02872456798ee8039e04f5a992de5bb98", "fileid": "4eb4efbf3b0ff3e2c5a4f046eee8182f2957066df6738d6ec2bfa7bd9fb94f8e", "status": "success", "check": "OK", "buildurl": "https://github.com/r-universe/ulrichriegel/actions/runs/26506805164" }, { "r": "4.6.0", "os": "linux", "version": "2.4.5", "date": "2026-05-27T10:57:34.000Z", "distro": "noble", "commit": "4da101e02872456798ee8039e04f5a992de5bb98", "fileid": "b927c109e40fb74023f65c9f89b1c427d00e8d0c8a9f42351db50c5bccad08de", "status": "success", "check": "OK", "buildurl": "https://github.com/r-universe/ulrichriegel/actions/runs/26506805164" }, { "r": "4.5.3", "os": "mac", "version": "2.4.5", "date": "2026-05-27T10:56:55.000Z", "commit": "4da101e02872456798ee8039e04f5a992de5bb98", "fileid": "e937cf10ba6e31a18b42a02f005d04caaeef91981ea8bd18b2eda659258568b4", "status": "success", "check": "OK", "buildurl": "https://github.com/r-universe/ulrichriegel/actions/runs/26506805164" }, { "r": "4.6.0", "os": "mac", "version": "2.4.5", "date": "2026-05-27T10:57:17.000Z", "commit": "4da101e02872456798ee8039e04f5a992de5bb98", "fileid": "ee29efe10259322db27b89b37af79ebbd28e6e78eaf714216f300dd158ce1071", "status": "success", "check": "OK", "buildurl": "https://github.com/r-universe/ulrichriegel/actions/runs/26506805164" }, { "r": "4.6.0", "os": "wasm", "version": "2.4.5", "date": "2026-05-27T10:57:29.000Z", "commit": "4da101e02872456798ee8039e04f5a992de5bb98", "fileid": "1706c341a8dcc3c3b2882e10850a1eec235567f9e8294feb8b1d98504b7c26b4", "status": "success", "buildurl": "https://github.com/r-universe/ulrichriegel/actions/runs/26506805164" }, { "r": "4.7.0", "os": "win", "version": "2.4.5", "date": "2026-05-27T10:57:01.000Z", "commit": "4da101e02872456798ee8039e04f5a992de5bb98", "fileid": "d520f86e80d2b7046e7ab46983644a602f842fe7a25c7e5f42903cfd5ab4d6b6", "status": "success", "check": "OK", "buildurl": "https://github.com/r-universe/ulrichriegel/actions/runs/26506805164" }, { "r": "4.5.3", "os": "win", "version": "2.4.5", "date": "2026-05-27T10:57:09.000Z", "commit": "4da101e02872456798ee8039e04f5a992de5bb98", "fileid": "b77b5c4071b8577ad5f6ea313ae7a56fb88f695e5e6bf5a02c0eba1fa263680c", "status": "success", "check": "OK", "buildurl": "https://github.com/r-universe/ulrichriegel/actions/runs/26506805164" }, { "r": "4.6.0", "os": "win", "version": "2.4.5", "date": "2026-05-27T10:57:28.000Z", "commit": "4da101e02872456798ee8039e04f5a992de5bb98", "fileid": "c1700e9123f4225728189ca01e6d43bfdc13a86539307e829d35f3edf580338b", "status": "success", "check": "OK", "buildurl": "https://github.com/r-universe/ulrichriegel/actions/runs/26506805164" } ] }