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  "Version": "1.0.16",
  "Date": "2026-02-27",
  "Title": "Functions from \"Reinsurance: Actuarial and Statistical Aspects\"",
  "Description": "Functions from the book \"Reinsurance: Actuarial and\nStatistical Aspects\" (2017) by Hansjoerg Albrecher, Jan\nBeirlant and Jef Teugels\n<https://www.wiley.com/en-us/Reinsurance%3A+Actuarial+and+Statistical+Aspects-p-9780470772683>.",
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  "Maintainer": "Tom Reynkens <tomreynkens.r@gmail.com>",
  "License": "GPL (>= 2)",
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  "Repository": "https://treynkens.r-universe.dev",
  "Date/Publication": "2026-02-27 18:25:59 UTC",
  "RemoteUrl": "https://github.com/treynkens/reins",
  "RemoteRef": "HEAD",
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  "Packaged": {
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  "Author": "Tom Reynkens [aut, cre] (ORCID:\n<https://orcid.org/0000-0002-5516-5107>),\nRoel Verbelen [aut] (R code for Mixed Erlang distribution, ORCID:\n<https://orcid.org/0000-0002-2347-9240>),\nAnastasios Bardoutsos [ctb] (Original R code for cEPD estimator),\nDries Cornilly [ctb] (Original R code for EVT estimators for truncated\ndata),\nYuri Goegebeur [ctb] (Original S-Plus code for basic EVT estimators),\nKlaus Herrmann [ctb] (Original R code for GPD estimator)",
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    "cExpQQ",
    "cgenHill",
    "cGPDmle",
    "cHill",
    "cLognormalQQ",
    "cMoment",
    "cParetoQQ",
    "cPOT",
    "cProb",
    "cProbEPD",
    "cProbGH",
    "cProbGPD",
    "cProbMOM",
    "cQuant",
    "cQuantGH",
    "cQuantGPD",
    "cQuantMOM",
    "cReturn",
    "cReturnEPD",
    "cReturnGH",
    "cReturnGPD",
    "cReturnMOM",
    "crHill",
    "crParetoQQ",
    "crSurv",
    "CTE",
    "cWeibullQQ",
    "dburr",
    "depd",
    "dfrechet",
    "dgpd",
    "dpareto",
    "dSplice",
    "dtburr",
    "dtexp",
    "dtfrechet",
    "dtgpd",
    "dtlnorm",
    "dtpareto",
    "dtweibull",
    "EPD",
    "EPDfit",
    "ES",
    "EVTfit",
    "ExcessEPD",
    "ExcessGPD",
    "ExcessHill",
    "ExcessPareto",
    "ExcessSplice",
    "ExpQQ",
    "generalizedQQ",
    "genHill",
    "genQQ",
    "GPDfit",
    "GPDmle",
    "GPDresiduals",
    "Hill",
    "Hill.2oQV",
    "Hill.kopt",
    "icHill",
    "icParetoQQ",
    "KaplanMeier",
    "LognormalQQ",
    "LognormalQQ_der",
    "LStail",
    "MeanExcess",
    "MeanExcess_TB",
    "MEfit",
    "Moment",
    "ParetoQQ",
    "ParetoQQ_der",
    "pburr",
    "pClas",
    "pEdge",
    "pepd",
    "pfrechet",
    "pGC",
    "pgpd",
    "POT",
    "ppareto",
    "Prob",
    "ProbEPD",
    "ProbGH",
    "ProbGPD",
    "ProbMOM",
    "ProbReg",
    "pSplice",
    "ptburr",
    "ptexp",
    "ptfrechet",
    "ptgpd",
    "ptlnorm",
    "ptpareto",
    "ptweibull",
    "qburr",
    "qepd",
    "qfrechet",
    "qgpd",
    "qpareto",
    "qSplice",
    "qtburr",
    "qtexp",
    "qtfrechet",
    "qtgpd",
    "qtlnorm",
    "qtpareto",
    "qtweibull",
    "Quant",
    "Quant.2oQV",
    "QuantGH",
    "QuantGPD",
    "QuantMOM",
    "QuantReg",
    "rburr",
    "repd",
    "Return",
    "ReturnEPD",
    "ReturnGH",
    "ReturnGPD",
    "ReturnMOM",
    "rfrechet",
    "rgpd",
    "rpareto",
    "rSplice",
    "rtburr",
    "rtexp",
    "rtfrechet",
    "rtgpd",
    "rtlnorm",
    "rtpareto",
    "rtweibull",
    "Scale",
    "Scale.2o",
    "ScaleEPD",
    "ScaleReg",
    "SpliceECDF",
    "SpliceFit",
    "SpliceFitGPD",
    "SpliceFitHill",
    "SpliceFiticPareto",
    "SpliceFitPareto",
    "SpliceLL",
    "SpliceLL_TB",
    "SplicePP",
    "SplicePP_TB",
    "SpliceQQ",
    "SpliceQQ_TB",
    "SpliceTB",
    "stdf",
    "stdf2",
    "trDT",
    "trDTMLE",
    "trEndpoint",
    "trEndpointMLE",
    "trHill",
    "trMLE",
    "trParetoQQ",
    "trProb",
    "trProbMLE",
    "trQuant",
    "trQuantMLE",
    "trQuantW",
    "trTest",
    "trTestMLE",
    "TSfraction",
    "Turnbull",
    "VaR",
    "WeibullQQ",
    "WeibullQQ_der",
    "Weissman.p",
    "Weissman.q",
    "Weissman.q.2oQV",
    "Weissman.r"
  ],
  "_datasets": [
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      "name": "norwegianfire",
      "title": "Norwegian fire insurance data",
      "object": "norwegianfire",
      "file": "norwegianfire.RData",
      "class": [
        "data.frame"
      ],
      "fields": [
        "size",
        "year"
      ],
      "rows": 9181,
      "table": true,
      "tojson": true
    },
    {
      "name": "secura",
      "title": "Secura dataset",
      "object": "secura",
      "file": "secura.RData",
      "class": [
        "data.frame"
      ],
      "fields": [
        "year",
        "size"
      ],
      "rows": 371,
      "table": true,
      "tojson": true
    },
    {
      "name": "soa",
      "title": "SOA Group Medical Insurance Large Claims Database",
      "object": "soa",
      "file": "soa.RData",
      "class": [
        "data.frame"
      ],
      "fields": [
        "size"
      ],
      "rows": 75789,
      "table": true,
      "tojson": true
    }
  ],
  "_help": [
    {
      "page": "Burr",
      "title": "The Burr distribution",
      "topics": [
        "dburr",
        "pburr",
        "qburr",
        "rburr"
      ]
    },
    {
      "page": "cEPD",
      "title": "EPD estimator for right censored data",
      "topics": [
        "cEPD"
      ]
    },
    {
      "page": "cExpQQ",
      "title": "Exponential quantile plot for right censored data",
      "topics": [
        "cExpQQ"
      ]
    },
    {
      "page": "cgenHill",
      "title": "Generalised Hill estimator for right censored data",
      "topics": [
        "cgenHill"
      ]
    },
    {
      "page": "cGPD",
      "title": "GPD-ML estimator for right censored data",
      "topics": [
        "cGPDmle",
        "cPOT"
      ]
    },
    {
      "page": "cHill",
      "title": "Hill estimator for right censored data",
      "topics": [
        "cHill"
      ]
    },
    {
      "page": "cLognormalQQ",
      "title": "Log-normal quantile plot for right censored data",
      "topics": [
        "cLognormalQQ"
      ]
    },
    {
      "page": "cMoment",
      "title": "MOM estimator for right censored data",
      "topics": [
        "cMoment"
      ]
    },
    {
      "page": "cParetoQQ",
      "title": "Pareto quantile plot for right censored data",
      "topics": [
        "cParetoQQ"
      ]
    },
    {
      "page": "cProb",
      "title": "Estimator of small exceedance probabilities and large return periods using censored Hill",
      "topics": [
        "cProb",
        "cReturn"
      ]
    },
    {
      "page": "cProbEPD",
      "title": "Estimator of small exceedance probabilities and large return periods using censored EPD",
      "topics": [
        "cProbEPD",
        "cReturnEPD"
      ]
    },
    {
      "page": "cProbGH",
      "title": "Estimator of small exceedance probabilities and large return periods using censored generalised Hill",
      "topics": [
        "cProbGH",
        "cReturnGH"
      ]
    },
    {
      "page": "cProbGPD",
      "title": "Estimator of small exceedance probabilities and large return periods using censored GPD-MLE",
      "topics": [
        "cProbGPD",
        "cReturnGPD"
      ]
    },
    {
      "page": "cProbMOM",
      "title": "Estimator of small exceedance probabilities and large return periods using censored MOM",
      "topics": [
        "cProbMOM",
        "cReturnMOM"
      ]
    },
    {
      "page": "cQuant",
      "title": "Estimator of large quantiles using censored Hill",
      "topics": [
        "cQuant"
      ]
    },
    {
      "page": "cQuantGH",
      "title": "Estimator of large quantiles using censored Hill",
      "topics": [
        "cQuantGH"
      ]
    },
    {
      "page": "cQuantGPD",
      "title": "Estimator of large quantiles using censored GPD-MLE",
      "topics": [
        "cQuantGPD"
      ]
    },
    {
      "page": "cQuantMOM",
      "title": "Estimator of large quantiles using censored MOM",
      "topics": [
        "cQuantMOM"
      ]
    },
    {
      "page": "crHill",
      "title": "Hill-type estimator for the conditional EVI",
      "topics": [
        "crHill"
      ]
    },
    {
      "page": "crParetoQQ",
      "title": "Conditional Pareto quantile plot for right censored data",
      "topics": [
        "crParetoQQ"
      ]
    },
    {
      "page": "crSurv",
      "title": "Non-parametric estimator of conditional survival function",
      "topics": [
        "crSurv"
      ]
    },
    {
      "page": "CTE",
      "title": "Conditional Tail Expectation",
      "topics": [
        "CTE",
        "ES"
      ]
    },
    {
      "page": "cWeibullQQ",
      "title": "Weibull quantile plot for right censored data",
      "topics": [
        "cWeibullQQ"
      ]
    },
    {
      "page": "EPD",
      "title": "EPD estimator",
      "topics": [
        "EPD"
      ]
    },
    {
      "page": "EPDfit",
      "title": "Fit EPD using MLE",
      "topics": [
        "EPDfit"
      ]
    },
    {
      "page": "EVTfit",
      "title": "EVT fit",
      "topics": [
        "EVTfit"
      ]
    },
    {
      "page": "ExcessEPD",
      "title": "Estimates for excess-loss premiums using EPD estimates",
      "topics": [
        "ExcessEPD"
      ]
    },
    {
      "page": "ExcessGPD",
      "title": "Estimates for excess-loss premiums using GPD-MLE estimates",
      "topics": [
        "ExcessGPD"
      ]
    },
    {
      "page": "ExcessPareto",
      "title": "Estimates for excess-loss premiums using a Pareto model",
      "topics": [
        "ExcessHill",
        "ExcessPareto"
      ]
    },
    {
      "page": "ExcessSplice",
      "title": "Estimates for excess-loss premiums using splicing",
      "topics": [
        "ExcessSplice"
      ]
    },
    {
      "page": "ExpQQ",
      "title": "Exponential quantile plot",
      "topics": [
        "ExpQQ"
      ]
    },
    {
      "page": "EPdist",
      "title": "The Extended Pareto Distribution",
      "topics": [
        "depd",
        "pepd",
        "qepd",
        "repd"
      ]
    },
    {
      "page": "Frechet",
      "title": "The Frechet distribution",
      "topics": [
        "dfrechet",
        "pfrechet",
        "qfrechet",
        "rfrechet"
      ]
    },
    {
      "page": "genHill",
      "title": "Generalised Hill estimator",
      "topics": [
        "genHill"
      ]
    },
    {
      "page": "genQQ",
      "title": "Generalised quantile plot",
      "topics": [
        "generalizedQQ",
        "genQQ"
      ]
    },
    {
      "page": "GPD",
      "title": "The generalised Pareto distribution",
      "topics": [
        "dgpd",
        "pgpd",
        "qgpd",
        "rgpd"
      ]
    },
    {
      "page": "GPDfit",
      "title": "Fit GPD using MLE",
      "topics": [
        "GPDfit"
      ]
    },
    {
      "page": "GPDmle",
      "title": "GPD-ML estimator",
      "topics": [
        "GPDmle",
        "POT"
      ]
    },
    {
      "page": "GPDresiduals",
      "title": "GPD residual plot",
      "topics": [
        "GPDresiduals"
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      "page": "Hill",
      "title": "Hill estimator",
      "topics": [
        "Hill"
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      "page": "Hill2oQV",
      "title": "Bias-reduced MLE (Quantile view)",
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        "Hill.2oQV"
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      "page": "Hill.kopt",
      "title": "Select optimal threshold for Hill estimator",
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        "Hill.kopt"
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      "page": "icParetoQQ",
      "title": "Pareto quantile plot for interval censored data",
      "topics": [
        "icParetoQQ"
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    {
      "page": "KaplanMeier",
      "title": "Kaplan-Meier estimator",
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        "KaplanMeier"
      ]
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      "page": "LognormalQQ",
      "title": "Log-normal quantile plot",
      "topics": [
        "LognormalQQ"
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      "page": "LognormalQQ_der",
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      "topics": [
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    {
      "page": "LStail",
      "title": "Least Squares tail estimator",
      "topics": [
        "LStail",
        "TSfraction"
      ]
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    {
      "page": "MeanExcess",
      "title": "Mean excess function",
      "topics": [
        "MeanExcess"
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    {
      "page": "MeanExcess_TB",
      "title": "Mean excess function using Turnbull estimator",
      "topics": [
        "MeanExcess_TB"
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    },
    {
      "page": "MEfit",
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        "MEfit"
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    },
    {
      "page": "Moment",
      "title": "Moment estimator",
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        "Moment"
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    },
    {
      "page": "norwegianfire",
      "title": "Norwegian fire insurance data",
      "topics": [
        "norwegianfire"
      ]
    },
    {
      "page": "Pareto",
      "title": "The Pareto distribution",
      "topics": [
        "dpareto",
        "ppareto",
        "qpareto",
        "rpareto"
      ]
    },
    {
      "page": "ParetoQQ",
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        "ParetoQQ"
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    {
      "page": "ParetoQQ_der",
      "title": "Derivative plot of the Pareto QQ-plot",
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    {
      "page": "pClas",
      "title": "Classical estimators for the CDF",
      "topics": [
        "pClas"
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      "page": "pEdge",
      "title": "Edgeworth approximation",
      "topics": [
        "pEdge"
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      "page": "pGC",
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      "page": "Prob",
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      "topics": [
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        "Return",
        "Weissman.p",
        "Weissman.r"
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    },
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        "ReturnEPD"
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      "page": "ProbGH",
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        "ReturnGH"
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      "page": "ProbGPD",
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        "ReturnGPD"
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    },
    {
      "page": "ProbMOM",
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        "ReturnMOM"
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    {
      "page": "ProbReg",
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    {
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      "title": "Weissman estimator of extreme quantiles",
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        "Weissman.q"
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      "page": "Quant2o",
      "title": "Second order refined Weissman estimator of extreme quantiles (QV)",
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        "Weissman.q.2oQV"
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      "page": "QuantGH",
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      "page": "QuantGPD",
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      "page": "QuantMOM",
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    },
    {
      "page": "QuantReg",
      "title": "Estimator of extreme quantiles in regression",
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        "QuantReg"
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    },
    {
      "page": "Scale",
      "title": "Scale estimator",
      "topics": [
        "Scale"
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      "page": "Scale.2o",
      "title": "Bias-reduced scale estimator using second order Hill estimator",
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    {
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      "title": "Secura dataset",
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        "secura"
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    },
    {
      "page": "soa",
      "title": "SOA Group Medical Insurance Large Claims Database",
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    {
      "page": "Splice",
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        "pSplice",
        "qSplice",
        "rSplice"
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      "page": "SpliceECDF",
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      "page": "SpliceFit",
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        "SpliceFit"
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      "page": "SpliceFitGPD",
      "title": "Splicing of mixed Erlang and GPD using POT-MLE",
      "topics": [
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      ]
    },
    {
      "page": "SpliceFiticPareto",
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    },
    {
      "page": "SpliceFitPareto",
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        "SpliceFitPareto"
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    {
      "page": "SpliceLL",
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      "topics": [
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    },
    {
      "page": "SpliceLL_TB",
      "title": "LL-plot with fitted and Turnbull survival function",
      "topics": [
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      "page": "SplicePP",
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        "stdf2"
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    },
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    },
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    },
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    },
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    },
    {
      "page": "trDT",
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      "page": "trHill",
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    {
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      "title": "Estimator of small exceedance probabilities using truncated Hill",
      "topics": [
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    },
    {
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      "title": "Estimator of small exceedance probabilities using truncated MLE",
      "topics": [
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    },
    {
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      "title": "Estimator of large quantiles using truncated Hill",
      "topics": [
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        "trQuantW"
      ]
    },
    {
      "page": "trQuantMLE",
      "title": "Estimator of large quantiles using truncated MLE",
      "topics": [
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    },
    {
      "page": "trTest",
      "title": "Test for truncated Pareto-type tails",
      "topics": [
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    },
    {
      "page": "trTestMLE",
      "title": "Test for truncated GPD tails",
      "topics": [
        "trTestMLE"
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    },
    {
      "page": "Turnbull",
      "title": "Turnbull estimator",
      "topics": [
        "Turnbull"
      ]
    },
    {
      "page": "tWeibull",
      "title": "The truncated Weibull distribution",
      "topics": [
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    },
    {
      "page": "VaR",
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      "topics": [
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    {
      "source": "ReIns.Rmd",
      "filename": "ReIns.html",
      "title": "Using the ReIns package",
      "author": "Tom Reynkens",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Introduction",
        "Datasets",
        "Graphical methods",
        "Exponential QQ-plot",
        "Pareto QQ-plot",
        "Log-normal QQ-plot",
        "Weibull QQ-plot",
        "Estimators of the EVI",
        "Estimators of $\\gamma>0$",
        "General estimators",
        "Estimators of quantiles and return periods",
        "Estimators of quantiles",
        "Estimators of return periods",
        "Censored data",
        "Right censored data",
        "Interval censored data",
        "Global fits using splicing",
        "Fitting a spliced distribution",
        "Checking adequacy of fitted spliced distribution",
        "Risk measures",
        "Excess-loss premiums",
        "Value-at-Risk",
        "Conditional Tail Expectation",
        "Simulations",
        "Distributions",
        "Approximations of the distribution function",
        "Classical approximations",
        "Approximations using orthogonal polynomials",
        "References"
      ],
      "created": "2015-08-20 11:58:33",
      "modified": "2017-06-10 14:00:29",
      "commits": 45
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