Package: Pareto 2.4.5

Pareto: The Pareto, Piecewise Pareto and Generalized Pareto Distribution

Utilities for the Pareto, piecewise Pareto and generalized Pareto distribution that are useful for reinsurance pricing. In particular, the package provides a non-trivial algorithm that can be used to match the expected losses of a tower of reinsurance layers with a layer-independent collective risk model. The theoretical background of the matching algorithm and most other methods are described in Ulrich Riegel (2018) <doi:10.1007/s13385-018-0177-3>.

Authors:Ulrich Riegel [aut, cre]

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Pareto.pdf |Pareto.html✨
Pareto/json (API)
NEWS

# Install 'Pareto' in R:
install.packages('Pareto', repos = c('https://ulrichriegel.r-universe.dev', 'https://cloud.r-project.org'))

Bug tracker:https://github.com/ulrichriegel/pareto/issues

Datasets:

On CRAN:

Conda:

7.13 score 11 stars 1 packages 204 scripts 947 downloads 4 mentions 52 exports 0 dependencies

Last updated from:4da101e028. Checks:8 OK. Indexed: yes.

TargetResultTimeFilesSyslog
linux-devel-x86_64OK129
source / vignettesOK164
linux-release-x86_64OK135
macos-devel-arm64OK150
macos-release-arm64OK138
windows-develOK96
windows-releaseOK153
wasm-releaseOK97

Exports:dGenParetodParetodPiecewiseParetoExcess_FrequencyFit_PML_CurveFit_ReferencesGenPareto_Layer_MeanGenPareto_Layer_SMGenPareto_Layer_VarGenPareto_ML_Estimator_Alphais.PGP_Modelis.PPP_Modelis.valid.PGP_Modelis.valid.PPP_ModelLayer_MeanLayer_SdLayer_VarLocal_Pareto_AlphaPareto_CDFPareto_ExtrapolationPareto_Find_Alpha_btw_FQ_LayerPareto_Find_Alpha_btw_FQsPareto_Find_Alpha_btw_LayersPareto_Layer_MeanPareto_Layer_SMPareto_Layer_VarPareto_ML_Estimator_AlphaPareto_PDFpGenParetoPGP_ModelPiecewisePareto_CDFPiecewisePareto_Layer_MeanPiecewisePareto_Layer_SMPiecewisePareto_Layer_VarPiecewisePareto_Match_Layer_LossesPiecewisePareto_ML_Estimator_AlphaPiecewisePareto_PDFpParetopPiecewiseParetoPPP_ModelPPP_Model_Excess_FrequencyPPP_Model_Exp_Layer_LossPPP_Model_Layer_SdPPP_Model_Layer_VarPPP_Model_SimulateqGenParetoqParetoqPiecewiseParetorGenParetorParetorPiecewiseParetoSimulate_Losses

Dependencies:

Pareto Package Vignette

Ulrich Riegel

Rendered fromPareto.Rmdusingknitr::rmarkdownon Mar 27 2026.

Last update: 2021-02-18
Started: 2019-11-16

Readme and manuals

Help Manual

Help pageTopics
Density of the generalized Pareto DistributiondGenPareto
Density of the Pareto DistributiondPareto
Density of the Piecewise Pareto DistributiondPiecewisePareto
Example data: Attachment PointsExample1_AP
Example data: Expected LossesExample1_EL
Expected Frequency in Excess of a ThresholdExcess_Frequency
Expected Frequency in Excess of a ThresholdExcess_Frequency.PGP_Model
Expected Frequency in Excess of a ThresholdExcess_Frequency.PPP_Model
Fits a Collective Model to a PML CurveFit_PML_Curve
Fit a Collective Model to a Wishlist of ReferencesFit_References
Layer Mean of the generalized Pareto DistributionGenPareto_Layer_Mean
Second Layer Moment of the Generalized Pareto DistributionGenPareto_Layer_SM
Layer Variance of the Generalized Pareto DistributionGenPareto_Layer_Var
Maximum Likelihood Estimation of the Pareto Alphas of a Generalized Pareto DistributionGenPareto_ML_Estimator_Alpha
Check if an object is a PGP_Modelis.PGP_Model
Check if an object is a PPP_Modelis.PPP_Model
Check if an object is a valid PGP_Modelis.valid.PGP_Model
Check if an object is a valid PPP_Modelis.valid.PPP_Model
Expected Loss of a Reinsurance LayerLayer_Mean
Expected Loss of a Reinsurance LayerLayer_Mean.PGP_Model
Expected Loss of a Reinsurance LayerLayer_Mean.PPP_Model
Standard Deviation of a Reinsurance LayerLayer_Sd
Standard Deviation of a Reinsurance LayerLayer_Sd.PGP_Model
Standard Deviation of a Reinsurance LayerLayer_Sd.PPP_Model
Variance of a Reinsurance LayerLayer_Var
Variance of a Reinsurance LayerLayer_Var.PGP_Model
Variance of a Reinsurance LayerLayer_Var.PPP_Model
Local Pareto AlphaLocal_Pareto_Alpha
Distribution Function of the Pareto DistributionPareto_CDF
Pareto ExtrapolationPareto_Extrapolation
Pareto Alpha Between a Frequency and a LayerPareto_Find_Alpha_btw_FQ_Layer
Pareto Alpha Between Two FrequenciesPareto_Find_Alpha_btw_FQs
Pareto Alpha Between Two LayersPareto_Find_Alpha_btw_Layers
Layer Mean of the Pareto DistributionPareto_Layer_Mean
Second Layer Moment of the Pareto DistributionPareto_Layer_SM
Layer Variance of the Pareto DistributionPareto_Layer_Var
Maximum Likelihood Estimation of the Alpha of a Pareto distributionPareto_ML_Estimator_Alpha
Density of the Pareto DistributionPareto_PDF
Distribution Function of the generalized Pareto DistributionpGenPareto
PGP_Model (Collective Panjer & Generalized Pareto Model) ObjectPGP_Model
Distribution Function of the Piecewise Pareto DistributionPiecewisePareto_CDF
Layer Mean of the Piecewise Pareto DistributionPiecewisePareto_Layer_Mean
Second Layer Moment of the Piecewise Pareto DistributionPiecewisePareto_Layer_SM
Layer Variance of the Piecewise Pareto DistributionPiecewisePareto_Layer_Var
Match a Tower of Expected Layers LossesPiecewisePareto_Match_Layer_Losses
Maximum Likelihood Estimation of the Alphas of the Piecewise Pareto DistributionPiecewisePareto_ML_Estimator_Alpha
Density of the Piecewise Pareto DistributionPiecewisePareto_PDF
Distribution Function of the Pareto DistributionpPareto
Distribution Function of the Piecewise Pareto DistributionpPiecewisePareto
PPP_Model (Collective Panjer & Piecewise Pareto Model) ObjectPPP_Model
Expected Frequency in Excess of a ThresholdPPP_Model_Excess_Frequency
Expected Loss of a Reinsurance LayerPPP_Model_Exp_Layer_Loss
Standard Deviation of a Reinsurance LayerPPP_Model_Layer_Sd
Variance of a Reinsurance LayerPPP_Model_Layer_Var
Simulate Losses with a PPP_ModelPPP_Model_Simulate
Print a PGP_Model Object (Collective Panjer & Generalized Pareto Model) Objectprint.PGP_Model
Print a PPP_Model Object (Collective Panjer & Piecewise Pareto Model) Objectprint.PPP_Model
Quantile Function of the generalized Pareto DistributionqGenPareto
Quantile Function of the Pareto DistributionqPareto
Quantile Function of the Piecewise Pareto DistributionqPiecewisePareto
Simulation of the generalized Pareto DistributionrGenPareto
Simulation of the Pareto DistributionrPareto
Simulation of the Piecewise Pareto DistributionrPiecewisePareto
Simulate Losses with a Collective ModelSimulate_Losses
Simulate Losses with a PGP_ModelSimulate_Losses.PGP_Model
Simulate Losses with a PPP_ModelSimulate_Losses.PPP_Model