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  "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<doi:10.1007/s13385-018-0177-3>.",
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  "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",
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  "Author": "Ulrich Riegel [aut, cre]",
  "Maintainer": "Ulrich Riegel <ulrich.riegel@gmx.de>",
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  "_published": "2026-10-18T06:55:13.168Z",
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      "date": "2019-12-17"
    },
    {
      "version": "1.1.3",
      "date": "2020-02-14"
    },
    {
      "version": "1.1.5",
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    {
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    "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": 6.320146286111054,
  "_indexed": true,
  "_nocasepkg": "pareto",
  "_universes": [
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