Package {NetSimR}

Type:	Package
Title:	Actuarial Functions for Non-Life Insurance Modelling
Version:	0.3.1
Description:	Assists actuaries and other insurance modellers in pricing, reserving and capital modelling for non-life insurance and reinsurance modelling. Provides functions that help model excess levels, capping and pure Incurred but not reported claims (pure IBNR). Includes capped mean, exposure curves and increased limit factor curves (ILFs) for LogNormal, Gamma, Pareto, Sliced LogNormal-Pareto and Sliced Gamma-Pareto distributions. Includes mean, probability density function (pdf), cumulative probability function (cdf) and inverse cumulative probability function for Sliced LogNormal-Pareto and Sliced Gamma-Pareto distributions. Includes calculating pure IBNR exposure with LogNormal and Gamma distribution for reporting delay. Includes three 'shiny' tools: a claims simulator with reinsurance structures, a generalised linear model fitting tool, and a claims frequency and severity distribution fitting tool. Methods used in the package refer to Free for All by Yiannis Parizas (2023) https://www.theactuary.com/2023/03/02/free-all; Escaping the triangle by Yiannis Parizas (2019) https://www.theactuary.com/features/2019/06/2019/06/05/escaping-triangle; Taken to excess by Yiannis Parizas (2019) https://www.theactuary.com/features/2019/03/2019/03/06/taken-excess.
License:	GPL-3
URL:	https://github.com/NetSimAnalytics/NetSimR
BugReports:	https://github.com/NetSimAnalytics/NetSimR/issues
Encoding:	UTF-8
Language:	en-GB
Imports:	shiny (≥ 1.8.1), base64enc, bslib (≥ 0.9.0), future (≥ 1.17.0), parallel, methods, stats, utils, graphics, grDevices
Suggests:	knitr, rmarkdown, crch, testthat (≥ 3.0.0), shinytest2, chromote, pkgload, DBI, RODBC, RPostgreSQL, RSQLite
VignetteBuilder:	knitr
Config/testthat/edition:	3
Config/roxygen2/version:	8.1.0
NeedsCompilation:	no
Packaged:	2026-09-22 06:32:39 UTC; yiann
Author:	Yiannis Parizas [aut, cre]
Maintainer:	Yiannis Parizas <yiannis.parizas@gmail.com>
Repository:	CRAN
Date/Publication:	2026-09-22 06:50:02 UTC

NetSimR: Actuarial Functions for Non-Life Insurance Modelling

Description

The NetSimR package provides five categories of functions:

1. Capped means, Exposure and ILF curves from various severity distributions, and the special functions behind them

2. Pure IBNR and UPR earned periods

3. Sliced distributions

4. Frequency-severity claims simulation, and applying a reinsurance layer to simulated claims

5. Shiny apps for simulating claims, fitting distributions and fitting GLMs

NetSimR special functions

IGamma erf

NetSimR mean functions

SlicedGammaParetoMean SlicedLNormParetoMean

NetSimR capped mean functions

GammaCappedMean LNormCappedMean ParetoCappedMean ParetoCappedMeanCalc SlicedGammaParetoCappedMean SlicedLNormParetoCappedMean

NetSimR exposure curve functions

ExposureCurveGamma ExposureCurveLNorm ExposureCurvePareto ExposureCurveSlicedGammaPareto ExposureCurveSlicedLNormPareto

NetSimR ILF curve functions

ILFGamma ILFLNorm ILFPareto ILFSlicedGammaPareto ILFSlicedLNormPareto

NetSimR pure IBNR functions

PureIBNRGamma PureIBNRLNorm

NetSimR Sliced distribution functions

dSlicedGammaPareto dSlicedLNormPareto pSlicedGammaPareto pSlicedLNormPareto qSlicedGammaPareto qSlicedLNormPareto

NetSimR claims simulation functions

simulate_claims simulate_function apply_deductible_limit

NetSimR Shiny apps

run_shiny_simulator run_shiny_distribution_fitting_tool run_shiny_glm_fitting_tool

Author(s)

Maintainer: Yiannis Parizas yiannis.parizas@gmail.com (ORCID)

Authors:

• Yiannis Parizas yiannis.parizas@gmail.com (ORCID)

See Also

Useful links:

• https://github.com/NetSimAnalytics/NetSimR

• Report bugs at https://github.com/NetSimAnalytics/NetSimR/issues

Exposure Curve from a Gamma severity distribution

Description

Gives the share of the expected claim cost of a Gamma severity distribution that falls below the amount x (the capped mean divided by the mean), as used to exposure rate a layer.

Usage

ExposureCurveGamma(x, shape, rate)

Arguments

Value

The value of the Exposure curve at x with Claim Severity from a Gamma distribution with parameters shape and rate. The arguments are recycled to a common length. A non-numeric argument, a negative x or a non-positive shape or rate is an error; NA values give NA.

See Also

Other exposure curve functions: ExposureCurveLNorm(), ExposureCurvePareto(), ExposureCurveSlicedGammaPareto(), ExposureCurveSlicedLNormPareto()

Examples

ExposureCurveGamma(700,1,0.0005)
ExposureCurveGamma(1000,1.5,0.0006)

Exposure Curve from a LogNormal severity distribution

Description

Gives the share of the expected claim cost of a LogNormal severity distribution that falls below the amount x (the capped mean divided by the mean), as used to exposure rate a layer.

Usage

ExposureCurveLNorm(x, mu, sigma)

Arguments

Value

The value of the Exposure curve at x with Claim Severity from a LogNormal distribution with parameters mu and sigma. An infinite x gives 1. The arguments are recycled to a common length. A non-numeric argument, a negative x or a non-positive sigma is an error; NA values give NA.

See Also

Other exposure curve functions: ExposureCurveGamma(), ExposureCurvePareto(), ExposureCurveSlicedGammaPareto(), ExposureCurveSlicedLNormPareto()

Examples

ExposureCurveLNorm(2000,6,1.5)
ExposureCurveLNorm(1000,5,1.6)

Exposure Curve from a Pareto severity distribution

Description

Gives the share of the expected claim cost of a Pareto severity distribution that falls below the amount x (the capped mean divided by the mean), as used to exposure rate a layer.

Usage

ExposureCurvePareto(x, scale, shape)

Arguments

Value

The value of the Exposure curve at x with Claim Severity from a Pareto distribution with parameters scale and shape. The exposure curve divides by the mean, which is infinite when shape <= 1; the function returns 0 in that case.

See Also

Other exposure curve functions: ExposureCurveGamma(), ExposureCurveLNorm(), ExposureCurveSlicedGammaPareto(), ExposureCurveSlicedLNormPareto()

Examples

ExposureCurvePareto(700,500,1.2)
ExposureCurvePareto(20000,200,1.1)

Exposure Curve from a Sliced Gamma Pareto severity distribution

Description

Gives the share of the expected claim cost of a sliced Gamma-Pareto severity distribution that falls below the amount x (the capped mean divided by the mean), as used to exposure rate a layer.

Usage

ExposureCurveSlicedGammaPareto(x, GShape, GRate, SlicePoint, PShape)

Arguments

Details

PShape is the Pareto shape parameter, usually written alpha; the sliced LogNormal-Pareto functions call the same parameter shape.

Value

The value of the Exposure curve at x with an attritional claim Gamma distribution with parameters GShape and GRate and a large claim Pareto distribution with parameters SlicePoint and PShape. The exposure curve divides by the mean, which is infinite when PShape <= 1 (and SlicePoint is finite); the function returns 0 in that case.

See Also

Other exposure curve functions: ExposureCurveGamma(), ExposureCurveLNorm(), ExposureCurvePareto(), ExposureCurveSlicedLNormPareto()

Examples

ExposureCurveSlicedGammaPareto(3000,1,0.0005,1000,1.2)
ExposureCurveSlicedGammaPareto(1000,1.1,0.0006,2000,1.6)
ExposureCurveSlicedGammaPareto(2000,1.2,0.0004,3000,1.4)

Exposure Curve from a Sliced LogNormal Pareto severity distribution

Description

Gives the share of the expected claim cost of a sliced LogNormal-Pareto severity distribution that falls below the amount x (the capped mean divided by the mean), as used to exposure rate a layer.

Usage

ExposureCurveSlicedLNormPareto(x, mu, sigma, SlicePoint, shape)

Arguments

Details

shape is the Pareto shape parameter, usually written alpha; the sliced Gamma-Pareto functions call the same parameter PShape.

Value

The value of the Exposure curve at x with an attritional claim LogNormal distribution with parameters mu and sigma and a large claim Pareto distribution with parameters SlicePoint and shape. The exposure curve divides by the mean, which is infinite when shape <= 1 (and SlicePoint is finite); the function returns 0 in that case.

See Also

Other exposure curve functions: ExposureCurveGamma(), ExposureCurveLNorm(), ExposureCurvePareto(), ExposureCurveSlicedGammaPareto()

Examples

ExposureCurveSlicedLNormPareto(1200,6,1.5,1000,1.2)
ExposureCurveSlicedLNormPareto(4000,7,1.6,3000,1.4)

Server function for the GLM Fitting tool application

Description

Runs a session of the GLM fitting tool: imports the data, fits the models, compares the stored ones, draws the actual against predicted chart and saves and loads the settings.

Usage

GLMFittingToolServer(input, output, session)

Arguments

Value

Called by shiny for its side effects, the outputs and observers of a session; the value is not used.

User interface of the Shiny GLM fitting tool

Description

Builds the pages of the GLM fitting tool: Welcome, Data, Model, Actual vs predicted and Save & load, with the theme switch.

Usage

GLMFittingToolUI(request)

Arguments

Details

A function of the request, so that it is built when the app starts, after every helper of the package is defined.

Value

The user interface of the application, a bslib navbar page.

Gamma capped mean

Description

Gives the expected claim amount when each claim from a Gamma severity distribution is capped at cap, as needed to price a policy limit or a reinsurance layer.

Usage

GammaCappedMean(cap, shape, rate)

Arguments

Value

The mean of the claim severity capped at cap with a Gamma distribution with parameters shape and rate. The arguments are recycled to a common length. A non-numeric argument, a negative cap or a non-positive shape or rate is an error; NA values give NA.

See Also

Other capped mean functions: LNormCappedMean(), ParetoCappedMean(), ParetoCappedMeanCalc(), SlicedGammaParetoCappedMean(), SlicedLNormParetoCappedMean()

Examples

GammaCappedMean(700,1,0.0005)
GammaCappedMean(1000,1.5,0.0006)

Upper incomplete gamma function

Description

Evaluates the upper incomplete gamma function, the integral of t^(a - 1) * exp(-t) from x to infinity, which appears in the closed form of the Gamma capped mean.

Usage

IGamma(a, x)

Arguments

Value

The value of the upper incomplete gamma function at x with shape parameter a, i.e. gamma(a) * pgamma(x, a, lower.tail = FALSE). The arguments are recycled to a common length. A non-numeric or non-positive a or a negative x is an error.

See Also

GammaCappedMean

Examples

IGamma(1,1)
IGamma(0.1,2)

Increased Limit Factor Curve from a Gamma severity distribution

Description

Gives the ratio of the Gamma capped mean at xHigh to that at xLow, the factor that takes the expected cost of a policy limit of xLow to that of a limit of xHigh.

Usage

ILFGamma(xLow, xHigh, shape, rate)

Arguments

Value

The value of the Increased Limit Factor curve from xLow to xHigh with Claim Severity from a Gamma distribution with parameters shape and rate.

See Also

Other ILF functions: ILFLNorm(), ILFPareto(), ILFSlicedGammaPareto(), ILFSlicedLNormPareto()

Examples

ILFGamma(700,1000,1,0.0005)
ILFGamma(1000,1200,1.5,0.0006)

Increased Limit Factor Curve from a LogNormal severity distribution

Description

Gives the ratio of the LogNormal capped mean at xHigh to that at xLow, the factor that takes the expected cost of a policy limit of xLow to that of a limit of xHigh.

Usage

ILFLNorm(xLow, xHigh, mu, sigma)

Arguments

Value

The value of the Increased Limit Factor curve from xLow to xHigh with Claim Severity from a LogNormal distribution with parameters mu and sigma.

See Also

Other ILF functions: ILFGamma(), ILFPareto(), ILFSlicedGammaPareto(), ILFSlicedLNormPareto()

Examples

ILFLNorm(1000,2000,6,1.5)
ILFLNorm(1000,1500,5,1.6)

Increased Limit Factor Curve from a Pareto severity distribution

Description

Gives the ratio of the Pareto capped mean at xHigh to that at xLow, the factor that takes the expected cost of a policy limit of xLow to that of a limit of xHigh.

Usage

ILFPareto(xLow, xHigh, scale, shape)

Arguments

Value

The value of the Increased Limit Factor curve from xLow to xHigh with Claim Severity from a Pareto distribution with parameters scale and shape.

See Also

Other ILF functions: ILFGamma(), ILFLNorm(), ILFSlicedGammaPareto(), ILFSlicedLNormPareto()

Examples

ILFPareto(700,1200,500,1.2)
ILFPareto(1200,20000,200,1.1)

Increased Limit Factor Curve from a Sliced Gamma Pareto severity distribution

Description

Gives the ratio of the sliced Gamma-Pareto capped mean at xHigh to that at xLow, the factor that takes the expected cost of a policy limit of xLow to that of a limit of xHigh.

Usage

ILFSlicedGammaPareto(xLow, xHigh, GShape, GRate, SlicePoint, PShape)

Arguments

Details

PShape is the Pareto shape parameter, usually written alpha; the sliced LogNormal-Pareto functions call the same parameter shape.

Value

The value of the Increased Limit Factor curve from xLow to xHigh with an attritional claim Gamma distribution with parameters GShape and GRate and a large claim Pareto distribution with parameters SlicePoint and PShape.

See Also

Other ILF functions: ILFGamma(), ILFLNorm(), ILFPareto(), ILFSlicedLNormPareto()

Examples

ILFSlicedGammaPareto(2000,3000,1,0.0005,1000,1.2)
ILFSlicedGammaPareto(800,1000,1.1,0.0006,2000,1.6)
ILFSlicedGammaPareto(1200,2000,1.2,0.0004,3000,1.4)

Increased Limit Factor Curve from a Sliced LogNormal Pareto severity distribution

Description

Gives the ratio of the sliced LogNormal-Pareto capped mean at xHigh to that at xLow, the factor that takes the expected cost of a policy limit of xLow to that of a limit of xHigh.

Usage

ILFSlicedLNormPareto(xLow, xHigh, mu, sigma, SlicePoint, shape)

Arguments

Details

shape is the Pareto shape parameter, usually written alpha; the sliced Gamma-Pareto functions call the same parameter PShape.

Value

The value of the Increased Limit Factor curve from xLow to xHigh with an attritional claim LogNormal distribution with parameters mu and sigma and a large claim Pareto distribution with parameters SlicePoint and shape.

See Also

Other ILF functions: ILFGamma(), ILFLNorm(), ILFPareto(), ILFSlicedGammaPareto()

Examples

ILFSlicedLNormPareto(800,1200,6,1.5,1000,1.2)
ILFSlicedLNormPareto(2000,4000,7,1.6,3000,1.4)

Lognormal capped mean

Description

Gives the expected claim amount when each claim from a LogNormal severity distribution is capped at cap, as needed to price a policy limit or a reinsurance layer.

Usage

LNormCappedMean(cap, mu, sigma)

Arguments

Value

The mean of the claim severity capped at cap with a LogNormal distribution with parameters mu and sigma. The arguments are recycled to a common length. A non-numeric argument, a negative cap or a non-positive sigma is an error; NA values give NA.

See Also

Other capped mean functions: GammaCappedMean(), ParetoCappedMean(), ParetoCappedMeanCalc(), SlicedGammaParetoCappedMean(), SlicedLNormParetoCappedMean()

Examples

LNormCappedMean(2000,6,1.5)
LNormCappedMean(1000,5,1.6)

Pareto capped mean

Description

Gives the expected claim amount when each claim from a Pareto severity distribution is capped at cap, as needed to price a policy limit or a reinsurance layer.

Usage

ParetoCappedMean(cap, scale, shape)

Arguments

Value

The mean of the claim severity capped at cap with a Pareto distribution with parameters scale and shape. A cap at or below scale is returned unchanged, as no claim is smaller than scale. The arguments are recycled to a common length. A non-numeric argument, a negative cap or a non-positive scale or shape is an error; NA values give NA.

See Also

Other capped mean functions: GammaCappedMean(), LNormCappedMean(), ParetoCappedMeanCalc(), SlicedGammaParetoCappedMean(), SlicedLNormParetoCappedMean()

Examples

ParetoCappedMean(600,200,1.2)
ParetoCappedMean(800,100,1)
ParetoCappedMean(1000,500,0.8)
ParetoCappedMean(50,100,2)

Pareto capped mean intermediary calculation

Description

Evaluates the closed-form expression (shape * scale - cap * (scale / cap)^shape) / (shape - 1) that the Pareto capped mean is built on, for checking or reusing the intermediate step.

Usage

ParetoCappedMeanCalc(cap, scale, shape)

Arguments

Value

An interim calculation for the mean of the claim severity capped at cap with a Pareto distribution with parameters scale and shape. It is the closed form for cap >= scale and shape != 1; use ParetoCappedMean for the capped mean itself. The arguments are recycled to a common length.

See Also

Other capped mean functions: GammaCappedMean(), LNormCappedMean(), ParetoCappedMean(), SlicedGammaParetoCappedMean(), SlicedLNormParetoCappedMean()

Examples

ParetoCappedMeanCalc(800,100,1.1)
ParetoCappedMeanCalc(1000,500,0.9)

Pure IBNR exposure from a Gamma reporting delay distribution

Description

Gives the unearned and pure IBNR exposure of each policy period at a valuation date, from a Gamma reporting delay, as needed to reserve for claims that have occurred but have not yet been reported.

Usage

PureIBNRGamma(IncDate, ExpDate, ValDate, shape, rate)

Arguments

Details

Durations are counted in days on each date's own calendar and clock: a POSIXct time of day counts as a fraction of a day, and daylight saving changes do not add fractions of a day, so Date and POSIXct dates (or a mix of them) give the same results.

Value

A data frame with the unearned and pure IBNR exposure of each period in days (UnearnedDuration, and PureIBNRDuration rounded to 2 decimals) and as proportions between 0 and 1 of the period's duration (UnearnedDurationRatio and PureIBNRDurationRatio, rounded to 5 decimals), where the reporting delay has a Gamma distribution with parameters shape and rate. The ratios are computed before the durations are rounded. A period of zero length (ExpDate equal to IncDate) gives ratios of 0. The dates and parameters are recycled to a common length, one row each; lengths that do not recycle are an error.

See Also

Other pure IBNR functions: PureIBNRLNorm()

Examples

Dates = data.frame(
    inceptionDate = c("01/01/2006", "01/07/2006", "01/01/2007")
    ,expiryDate = c("31/12/2006", "30/06/2007", "31/12/2007")
)

Dates$inceptionDate<-as.POSIXct(Dates$inceptionDate, format="%d/%m/%Y")

Dates$expiryDate<-as.POSIXct(Dates$expiryDate, format="%d/%m/%Y")

ValuationDate<-as.POSIXct("30/10/2007", format="%d/%m/%Y")

PureIBNRGamma(Dates$inceptionDate,Dates$expiryDate,ValuationDate,7,0.15)

Pure IBNR exposure from a LogNormal reporting delay distribution

Description

Gives the unearned and pure IBNR exposure of each policy period at a valuation date, from a LogNormal reporting delay, as needed to reserve for claims that have occurred but have not yet been reported.

Usage

PureIBNRLNorm(IncDate, ExpDate, ValDate, mu, sigma)

Arguments

Details

Durations are counted in days on each date's own calendar and clock: a POSIXct time of day counts as a fraction of a day, and daylight saving changes do not add fractions of a day, so Date and POSIXct dates (or a mix of them) give the same results.

Value

A data frame with the unearned and pure IBNR exposure of each period in days (UnearnedDuration, and PureIBNRDuration rounded to 2 decimals) and as proportions between 0 and 1 of the period's duration (UnearnedDurationRatio and PureIBNRDurationRatio, rounded to 5 decimals), where the reporting delay has a LogNormal distribution with parameters mu and sigma. The ratios are computed before the durations are rounded. A period of zero length (ExpDate equal to IncDate) gives ratios of 0. The dates and parameters are recycled to a common length, one row each; lengths that do not recycle are an error.

See Also

Other pure IBNR functions: PureIBNRGamma()

Examples

Dates = data.frame(
    inceptionDate = c("01/01/2006", "01/07/2006", "01/01/2007")
    ,expiryDate = c("31/12/2006", "30/06/2007", "31/12/2007")
)

Dates$inceptionDate<-as.POSIXct(Dates$inceptionDate, format="%d/%m/%Y")

Dates$expiryDate<-as.POSIXct(Dates$expiryDate, format="%d/%m/%Y")

ValuationDate<-as.POSIXct("30/10/2007", format="%d/%m/%Y")

PureIBNRLNorm(Dates$inceptionDate,Dates$expiryDate,ValuationDate,4,1.5)

Sliced Gamma Pareto capped mean

Description

Gives the expected claim amount when each claim from a sliced severity distribution, with Gamma attritional claims below the slice point and a Pareto tail above it, is capped at cap.

Usage

SlicedGammaParetoCappedMean(cap, GShape, GRate, SlicePoint, PShape)

Arguments

Details

PShape is the Pareto shape parameter, usually written alpha; the sliced LogNormal-Pareto functions call the same parameter shape.

Value

The mean of the claim severity capped at cap with an attritional claim Gamma distribution with parameters GShape and GRate and a large claim Pareto distribution with parameters SlicePoint and PShape. A non-numeric argument, a negative cap or a non-positive parameter is an error; NA values give NA.

See Also

Other capped mean functions: GammaCappedMean(), LNormCappedMean(), ParetoCappedMean(), ParetoCappedMeanCalc(), SlicedLNormParetoCappedMean()

Examples

SlicedGammaParetoCappedMean(3000,1,0.0005,1000,1.2)
SlicedGammaParetoCappedMean(1000,1.1,0.0006,2000,1.6)
SlicedGammaParetoCappedMean(2000,1.2,0.0004,3000,1.4)

Sliced Gamma Pareto mean

Description

Gives the expected claim amount of a sliced severity distribution, with Gamma attritional claims below the slice point and a Pareto tail above it.

Usage

SlicedGammaParetoMean(GShape, GRate, SlicePoint, PShape)

Arguments

Details

PShape is the Pareto shape parameter, usually written alpha; the sliced LogNormal-Pareto functions call the same parameter shape.

Value

The mean of the claim severity with an attritional claim Gamma distribution with parameters GShape and GRate and a large claim Pareto distribution with parameters SlicePoint and PShape. The mean is Inf when PShape <= 1 (and SlicePoint is finite), as the Pareto tail then has no finite mean. A non-numeric or non-positive parameter is an error; NA values give NA.

See Also

Other sliced distribution functions: SlicedLNormParetoMean(), dSlicedGammaPareto(), dSlicedLNormPareto(), pSlicedGammaPareto(), pSlicedLNormPareto(), qSlicedGammaPareto(), qSlicedLNormPareto()

Examples

SlicedGammaParetoMean(1,0.0005,1000,1.2)
SlicedGammaParetoMean(1.1,0.0006,2000,1.6)
SlicedGammaParetoMean(1.2,0.0004,3000,1.4)

Sliced LogNormal Pareto capped mean

Description

Gives the expected claim amount when each claim from a sliced severity distribution, with LogNormal attritional claims below the slice point and a Pareto tail above it, is capped at cap.

Usage

SlicedLNormParetoCappedMean(cap, mu, sigma, SlicePoint, shape)

Arguments

Details

shape is the Pareto shape parameter, usually written alpha; the sliced Gamma-Pareto functions call the same parameter PShape.

Value

The mean of the claim severity capped at cap with an attritional claim LogNormal distribution with parameters mu and sigma and a large claim Pareto distribution with parameters SlicePoint and shape. A non-numeric argument, a negative cap or a non-positive sigma, SlicePoint or shape is an error; NA values give NA.

See Also

Other capped mean functions: GammaCappedMean(), LNormCappedMean(), ParetoCappedMean(), ParetoCappedMeanCalc(), SlicedGammaParetoCappedMean()

Examples

SlicedLNormParetoCappedMean(1200,6,1.5,1000,1.2)
SlicedLNormParetoCappedMean(2500,6.5,1.4,2000,1.6)
SlicedLNormParetoCappedMean(4000,7,1.6,3000,1.4)

Sliced LogNormal Pareto mean

Description

Gives the expected claim amount of a sliced severity distribution, with LogNormal attritional claims below the slice point and a Pareto tail above it.

Usage

SlicedLNormParetoMean(mu, sigma, SlicePoint, shape)

Arguments

Details

shape is the Pareto shape parameter, usually written alpha; the sliced Gamma-Pareto functions call the same parameter PShape.

Value

The mean of the claim severity with an attritional claim LogNormal distribution with parameters mu and sigma and a large claim Pareto distribution with parameters SlicePoint and shape. The mean is Inf when shape <= 1 (and SlicePoint is finite), as the Pareto tail then has no finite mean. A non-numeric argument or a non-positive sigma, SlicePoint or shape is an error; NA values give NA.

See Also

Other sliced distribution functions: SlicedGammaParetoMean(), dSlicedGammaPareto(), dSlicedLNormPareto(), pSlicedGammaPareto(), pSlicedLNormPareto(), qSlicedGammaPareto(), qSlicedLNormPareto()

Examples

SlicedLNormParetoMean(6,1.5,1000,1.2)
SlicedLNormParetoMean(6.5,1.4,2000,1.6)
SlicedLNormParetoMean(7,1.6,3000,1.4)

Apply a deductible and limit to claims

Description

Works out what a reinsurance structure cedes (or, for an excluded layer, leaves) of each claim, for pricing a layer or checking the simulator's figures by hand.

Usage

apply_deductible_limit(
  gross_claims_data,
  reinsurance_structure,
  deductible,
  limit
)

Arguments

Value

A vector with one value per claim: for 'Unlimited Layer' and 'Limited Layer', the amount ceded to the layer; for 'Exclude Layer', the claims with the layer taken out (the claims less what a 'Limited Layer' with the same deductible and limit would cede); for 'No Reinsurance Structure', the claims unchanged. Stops with an error when a deductible or limit the structure uses is negative.

Examples

apply_deductible_limit(c(100, 50, 20), 'Limited Layer', 40, 20)
apply_deductible_limit(c(100, 50, 20), 'Limited Layer', 10, 30)
apply_deductible_limit(c(100, 50, 20), 'Exclude Layer', 40, 20)

The probability density function (pdf) of a Sliced Gamma Pareto severity distribution

Description

Gives the probability density at the claim amount x of a sliced severity distribution, with Gamma attritional claims below the slice point and a Pareto tail above it.

Usage

dSlicedGammaPareto(x, GShape, GRate, SlicePoint, PShape)

Arguments

Details

PShape is the Pareto shape parameter, usually written alpha; the sliced LogNormal-Pareto functions call the same parameter shape.

Value

The value of the probability density function (pdf) at x with an attritional claim Gamma distribution with parameters GShape and GRate and a large claim Pareto distribution with parameters SlicePoint and PShape. A non-numeric argument or a non-positive parameter is an error; NA values give NA.

See Also

Other sliced distribution functions: SlicedGammaParetoMean(), SlicedLNormParetoMean(), dSlicedLNormPareto(), pSlicedGammaPareto(), pSlicedLNormPareto(), qSlicedGammaPareto(), qSlicedLNormPareto()

Examples

dSlicedGammaPareto(3000,1,0.0005,1000,1.2)
dSlicedGammaPareto(1000,1.1,0.0006,2000,1.6)
dSlicedGammaPareto(2000,1.2,0.0004,3000,1.4)

The probability density function (pdf) of a Sliced LogNormal Pareto severity distribution

Description

Gives the probability density at the claim amount x of a sliced severity distribution, with LogNormal attritional claims below the slice point and a Pareto tail above it.

Usage

dSlicedLNormPareto(x, mu, sigma, SlicePoint, shape)

Arguments

Details

shape is the Pareto shape parameter, usually written alpha; the sliced Gamma-Pareto functions call the same parameter PShape.

Value

The value of the probability density function (pdf) at x with an attritional claim LogNormal distribution with parameters mu and sigma and a large claim Pareto distribution with parameters SlicePoint and shape. A non-numeric argument or a non-positive sigma, SlicePoint or shape is an error; NA values give NA.

See Also

Other sliced distribution functions: SlicedGammaParetoMean(), SlicedLNormParetoMean(), dSlicedGammaPareto(), pSlicedGammaPareto(), pSlicedLNormPareto(), qSlicedGammaPareto(), qSlicedLNormPareto()

Examples

dSlicedLNormPareto(1200,6,1.5,1000,1.2)
dSlicedLNormPareto(4000,7,1.6,3000,1.4)

The class of the distribution objects

Description

Each object describes one frequency or severity distribution of the simulator: its parameters (ids used as app input ids, labels, allowed ranges and whether they must be whole numbers) and the functions the simulator needs. simulate_func draws values; moments_func gives the mean and standard deviation. Severity distributions also have survival_func and tail_quantile_func (the upper-tail probability and its inverse), used to splice Pareto tails and to draw only the claims that reach a layer, and optionally sum_func, which draws the total of a given number of claims in one step. Frequency distributions may have split_func, which draws the number of claims and how many of them are large. Allowed ranges are param_min_values and param_max_values (NA for no bound), with param_min_strict and param_max_strict marking bounds the value may not equal.

Server function for the Distribution Fitting tool application

Description

Reads the uploaded file, fits the frequency, severity, sliced and piecewise Pareto models the user asks for and renders their tables and charts; paired with distribution_fitting_tool_UI by run_shiny_distribution_fitting_tool.

Usage

distribution_fitting_tool_Server(input, output, session)

Arguments

Value

Called by shiny for its side effects, the outputs and observers of a session; the value is not used.

User interface of the Shiny distribution fitting tool

Description

The page of the distribution fitting application: a welcome tab, the data upload and one tab for each analysis, with the settings beside the results. It is built when the package is installed; run_shiny_distribution_fitting_tool pairs it with distribution_fitting_tool_Server.

Usage

distribution_fitting_tool_UI

Value

The user interface of the application, a bslib navbar page.

Error function

Description

Evaluates the Gauss error function, 2 * pnorm(sqrt(2) * x) - 1, which appears in the closed form of the LogNormal capped mean.

Usage

erf(x)

Arguments

Value

The value of the error function at x. A non-numeric x is an error.

See Also

LNormCappedMean

Examples

erf(0.1)
erf(0.5)

A vector with the frequency distribution objects

Description

A named list of distributionClass objects, one for each claim count distribution of the simulator: Poisson, Negative_Binomial, Binomial and Fixed_number_of_Counts. The names are the values accepted by the freqDistr argument of simulate_function(), and the objects hold the parameter ids, labels and ranges of the app's inputs and the functions that draw the claim counts.

Usage

freq_dist_options

Value

The frequency distribution objects.

A data frame with the frequency distribution parameter placeholders

Description

One row per parameter of the frequency distribution with the most parameters, giving the number and output id of the placeholder in which the simulator app renders that parameter's input for the chosen distribution.

Usage

freq_dist_parameter_placeholders

Value

The frequency distribution parameter placeholders.

Parameter to set the maximum number of Pareto slices

Description

The largest number of Pareto slices that the simulator app and simulate_claims accept, so that the app can build one row of slice inputs for each.

Usage

max_number_of_pareto_slices

Value

The maximum number of Pareto Slices.

The cumulative distribution function (cdf) of a Sliced Gamma-Pareto severity distribution

Description

Gives the probability that a claim from a sliced severity distribution, with Gamma attritional claims below the slice point and a Pareto tail above it, is at most x.

Usage

pSlicedGammaPareto(x, GShape, GRate, SlicePoint, PShape)

Arguments

Details

PShape is the Pareto shape parameter, usually written alpha; the sliced LogNormal-Pareto functions call the same parameter shape.

Value

The value of the cumulative distribution function (cdf) at x with an attritional claim Gamma distribution with parameters GShape and GRate and a large claim Pareto distribution with parameters SlicePoint and PShape. A non-numeric argument or a non-positive parameter is an error; NA values give NA.

See Also

Other sliced distribution functions: SlicedGammaParetoMean(), SlicedLNormParetoMean(), dSlicedGammaPareto(), dSlicedLNormPareto(), pSlicedLNormPareto(), qSlicedGammaPareto(), qSlicedLNormPareto()

Examples

pSlicedGammaPareto(3000,1,0.0005,1000,1.2)
pSlicedGammaPareto(1000,1.1,0.0006,2000,1.6)
pSlicedGammaPareto(2000,1.2,0.0004,3000,1.4)

The cumulative distribution function (cdf) of a Sliced LogNormal Pareto severity distribution

Description

Gives the probability that a claim from a sliced severity distribution, with LogNormal attritional claims below the slice point and a Pareto tail above it, is at most x.

Usage

pSlicedLNormPareto(x, mu, sigma, SlicePoint, shape)

Arguments

Details

shape is the Pareto shape parameter, usually written alpha; the sliced Gamma-Pareto functions call the same parameter PShape.

Value

The value of the cumulative distribution function (cdf) at x with an attritional claim LogNormal distribution with parameters mu and sigma and a large claim Pareto distribution with parameters SlicePoint and shape. A non-numeric argument or a non-positive sigma, SlicePoint or shape is an error; NA values give NA.

See Also

Other sliced distribution functions: SlicedGammaParetoMean(), SlicedLNormParetoMean(), dSlicedGammaPareto(), dSlicedLNormPareto(), pSlicedGammaPareto(), qSlicedGammaPareto(), qSlicedLNormPareto()

Examples

pSlicedLNormPareto(1200,6,1.5,1000,1.2)
pSlicedLNormPareto(4000,7,1.6,3000,1.4)

The inverse cumulative distribution function of a Sliced Gamma Pareto severity distribution

Description

Gives the claim amount that a claim from a sliced severity distribution, with Gamma attritional claims below the slice point and a Pareto tail above it, stays at or below with probability q; the inverse of pSlicedGammaPareto.

Usage

qSlicedGammaPareto(q, GShape, GRate, SlicePoint, PShape)

Arguments

Details

PShape is the Pareto shape parameter, usually written alpha; the sliced LogNormal-Pareto functions call the same parameter shape.

Value

The value of the inverse cumulative distribution function at q with an attritional claim Gamma distribution with parameters GShape and GRate and a large claim Pareto distribution with parameters SlicePoint and PShape. A non-numeric argument or a non-positive parameter is an error; NA values give NA.

See Also

Other sliced distribution functions: SlicedGammaParetoMean(), SlicedLNormParetoMean(), dSlicedGammaPareto(), dSlicedLNormPareto(), pSlicedGammaPareto(), pSlicedLNormPareto(), qSlicedLNormPareto()

Examples

qSlicedGammaPareto(0.5,1,0.0005,1000,1.2)
qSlicedGammaPareto(0.2,1.1,0.0006,2000,1.6)
qSlicedGammaPareto(0.8,1.2,0.0004,3000,1.4)

The inverse cumulative distribution function of a Sliced LogNormal Pareto severity distribution

Description

Gives the claim amount that a claim from a sliced severity distribution, with LogNormal attritional claims below the slice point and a Pareto tail above it, stays at or below with probability q; the inverse of pSlicedLNormPareto.

Usage

qSlicedLNormPareto(q, mu, sigma, SlicePoint, shape)

Arguments

Details

shape is the Pareto shape parameter, usually written alpha; the sliced Gamma-Pareto functions call the same parameter PShape.

Value

The value of the inverse cumulative distribution function at q with an attritional claim LogNormal distribution with parameters mu and sigma and a large claim Pareto distribution with parameters SlicePoint and shape. A non-numeric argument or a non-positive sigma, SlicePoint or shape is an error; NA values give NA.

See Also

Other sliced distribution functions: SlicedGammaParetoMean(), SlicedLNormParetoMean(), dSlicedGammaPareto(), dSlicedLNormPareto(), pSlicedGammaPareto(), pSlicedLNormPareto(), qSlicedGammaPareto()

Examples

qSlicedLNormPareto(0.5,6,1.5,1000,1.2)
qSlicedLNormPareto(0.7,7,1.6,3000,1.4)

A vector with the reinsurance structure options

Description

The names of the reinsurance structures that apply_deductible_limit and simulate_function accept, used by the simulator app as the choices of its structure inputs and to validate saved settings.

Usage

reinsurance_structures_options

Value

The reinsurance structure options

Run the distribution fitting application

Description

Opens NetDisFit, a shiny application that fits frequency and severity distributions to an uploaded claims file, compares them with the data, and splices Pareto tails onto a LogNormal body or fits a piecewise Pareto at chosen slicing points, ready for the NetSimR simulator.

Usage

run_shiny_distribution_fitting_tool()

Value

A shiny app object. Printing it, as happens when the function is called at the console, opens the application; it can also be passed to shiny::runApp().

See Also

run_shiny_simulator and run_shiny_glm_fitting_tool, the other two applications; SlicedLNormParetoMean, SlicedLNormParetoCappedMean, SlicedGammaParetoMean and SlicedGammaParetoCappedMean for the moments of the sliced distributions the tool fits.

Examples

if (interactive()) {
  run_shiny_distribution_fitting_tool()
}

Run the generalised linear model fitting application

Description

Opens a Shiny application that imports data from a CSV file or a database query, fits generalised linear models to it, compares the AIC of stored models, charts actual against predicted values and downloads the model and its predictions.

Usage

run_shiny_glm_fitting_tool()

Details

The formula typed in the application, or read from one of its settings files, is restricted to the columns of the imported data, numbers, the formula operators and a small set of formula functions: I(), log(), exp(), sqrt(), pmin(), pmax(), poly(), factor(), as.factor(), interaction() and offset(). Any other call is refused, so a settings file shared between colleagues cannot run code.

Value

A shiny app object. Printing it, as happens when the function is called at the console, opens the application; it can also be passed to shiny::runApp().

See Also

run_shiny_distribution_fitting_tool and run_shiny_simulator, the package's other applications.

Examples

if (interactive()) {
  run_shiny_glm_fitting_tool()
}

A function to run the shiny simulator application

Description

Opens the claims simulator, a Shiny app for running the frequency-severity model of simulate_function from a form, with charts, a report and saved settings, without writing any code.

Usage

run_shiny_simulator()

Value

A shiny app object (class shiny.appobj). Printing it, as happens when run_shiny_simulator() is called at the console, opens the app; pass it to shiny::runApp() to choose options such as the port.

See Also

simulate_claims and simulate_function, which run the same model from R code.

Examples

if (interactive()) {
  run_shiny_simulator()
}

A vector with the severity distribution objects

Description

A named list of distributionClass objects, one for each severity distribution of the simulator: Normal, LogNormal, Gamma, Exponential, Pareto and Fixed_Severity. The names are the values accepted by the sevDistr argument of simulate_function(). The Normal distribution has its own parameter ids (normal_mean, normal_sd), so that switching between the Normal and the Log-Normal in the app does not carry values across.

Usage

sev_dist_options

Value

The severity distribution objects.

A data frame with the severity distribution parameter placeholders

Description

One row per parameter of the severity distribution with the most parameters, giving the number and output id of the placeholder in which the simulator app renders that parameter's input for the chosen distribution.

Usage

sev_dist_parameter_placeholders

Value

The severity distribution parameter placeholders.

Server function for the Shiny Simulator application

Description

Builds the dynamic inputs of the claims simulator, runs the simulations when asked and serves the results tabs, the downloads and the saving and loading of settings; it is the server that run_shiny_simulator pairs with shiny_simulator_ui.

Usage

shiny_simulator_server(input, output, session)

Arguments

Value

Called by shiny for its side effects, the outputs and observers of a session; the value is not used.

User interface of the Shiny NetSimR simulator

Description

The page the simulator opens in: a welcome panel and the simulator itself, where the claim, reinsurance and run settings are entered and the results, charts and report are shown.

Usage

shiny_simulator_ui

Value

The user interface of the application, a bslib navbar page, which run_shiny_simulator pairs with shiny_simulator_server.

Simulate claims with a frequency-severity model

Description

A simpler interface to simulate_function, with short argument names and defaults for everything optional. Leaving an option out (NULL) switches the feature off: no seed, no Pareto slices, no cap, no reinstatement limit.

Usage

simulate_claims(
  n_sims,
  frequency,
  frequency_params,
  severity,
  severity_params,
  seed = NULL,
  truncate_at_zero = FALSE,
  pareto_thresholds = NULL,
  pareto_alphas = NULL,
  severity_cap = NULL,
  eel_layer = "none",
  eel_deductible = NULL,
  eel_limit = NULL,
  eel_reinstatements = NULL,
  agg_layer = "none",
  agg_deductible = NULL,
  agg_limit = NULL,
  parallel = FALSE,
  chunk_size = NULL,
  gross = TRUE,
  shortcuts = TRUE,
  progress = NULL
)

Arguments

Details

Distributions are chosen by name; case, spaces and underscores are ignored, so "Negative Binomial", "negative_binomial" and "Negative_Binomial" are the same. Their parameters are given in the order below, or named with these names:

Layers are "none", "unlimited" (everything above the deductible), "limited" (the limit excess of the deductible) or "exclude" (the claims with that layer removed). The each-and-every-loss layer applies to every claim; the aggregate layer applies to each simulation's total after the each-and-every-loss layer. The order is: severity cap -> each-and-every-loss layer per claim -> sum over the simulation -> aggregate deductible -> aggregate limit and reinstatement capacity. So with a "limited" each-and-every-loss layer and an "unlimited" or "limited" aggregate layer, the ceded total is min(max(S - agg_deductible, 0), agg_limit, (eel_reinstatements + 1) * eel_limit), where S is the sum of the layer's recoveries; three claims of 100 through a layer of 100 excess of 0 with no reinstatements and an aggregate deductible of 50 cede 100. An "exclude" aggregate layer is taken out of the recoveries after the reinstatement capacity has capped them. See simulate_function for the details.

Value

A data frame with one row per simulation, at full precision: claim_counts, total_claims (after the layers), gross_claims (before them, unless gross = FALSE) and, with limited reinstatements, number_of_reinstatements_used: the layer's recoveries in the simulation divided by eel_limit, capped at eel_reinstatements. The recoveries are taken after the aggregate deductible and limit of an "unlimited" or "limited" aggregate layer, but before an "exclude" aggregate layer is taken out: with an exclusion, the reinstatements are counted on the each-and-every-loss recoveries (after the reinstatement capacity). So three claims of 100 through a layer of 60 excess of 30 with two reinstatements and an "exclude" aggregate layer of 150 excess of 50 give a total of 50 but 2 reinstatements used.

See Also

simulate_function, which this calls, and run_shiny_simulator for the same model in an app.

Examples

# 10,000 years of Poisson claim counts with Log-Normal claim sizes
claims <- simulate_claims(
  10000, frequency = "Poisson", frequency_params = 3,
  severity = "LogNormal", severity_params = c(meanlog = 8, sdlog = 1.5), seed = 1
)
summary(claims$total_claims)

# a Pareto tail above 100,000, and a layer of 50,000 excess of 20,000 on each
# claim with two reinstatements
ceded <- simulate_claims(
  10000, "Poisson", 3, "LogNormal", c(8, 1.5), seed = 1,
  pareto_thresholds = 100000, pareto_alphas = 1.5,
  eel_layer = "limited", eel_deductible = 20000, eel_limit = 50000,
  eel_reinstatements = 2
)
mean(ceded$total_claims)

Simulate insurance claims with reinsurance structures

Description

A function to simulate frequency - severity of insurance claims using chunked vectorisation. The function applies severity cap, reinsurance structure for each and every loss claim, reinsurance structure for aggregate claims, and allows for piecewise Pareto slices

Usage

simulate_function(
  numOfSimulations,
  freq_params,
  sev_params,
  seedSetBinary = !is.null(seedValue),
  seedValue = NULL,
  freqDistr,
  sevDistr,
  paretoSlice = FALSE,
  pareto_slice_times = NULL,
  slice_pareto_alphas = NULL,
  slice_pareto_x_ms = NULL,
  sevCapBinary = FALSE,
  sev_cap_amount = NULL,
  reinsuranceStructureEEL = "No Reinsurance Structure",
  reinsurance_structure_eel_dedctible_amount = NULL,
  reinsurance_structure_eel_limit_amount = NULL,
  reinsuranceStructureAL = "No Reinsurance Structure",
  reinsurance_structure_al_dedctible_amount = NULL,
  reinsurance_structure_al_limit_amount = NULL,
  reinsuranceStructureLimitedReinstatements = FALSE,
  reinsuranceStructureReinstatementLimit = NULL,
  multiprocessing = FALSE,
  sevTruncateAtZero = FALSE,
  chunk_size = NULL,
  gross = TRUE,
  shortcuts = TRUE,
  progress = NULL
)

Arguments

Details

Order of the calculations, for each simulation (a period, e.g. a year): claims are drawn from the severity distribution (with its Pareto slices) and capped at the severity cap; the each-and-every-loss (EEL) structure applies to each claim; the results are summed over the period; then the aggregate deductible comes off that sum, and finally the aggregate limit and the reinstatement capacity cap what is left. In short: cap -> EEL layer per claim -> annual sum -> aggregate deductible -> aggregate limit and reinstatement capacity.

The reinstatement capacity applies to a 'Limited Layer' EEL structure with limited reinstatements, which pays at most (reinstatements + 1) * limit in a period. With an aggregate 'Unlimited Layer' or 'Limited Layer', the ceded total is min(max(S - aggregate deductible, 0), aggregate limit, (reinstatements + 1) * limit), where S is the sum of the period's EEL recoveries before any capacity (the market convention for an annual aggregate deductible). For example, three claims of 100 through a layer of 100 excess of 0 with no reinstatements and an aggregate deductible of 50 cede min(300 - 50, 100) = 100. Without an aggregate structure, the capacity caps S. With an aggregate 'Exclude Layer', the capacity caps S first and the aggregate layer is then taken out of the capped amount. An unlimited EEL layer, or limited reinstatements switched off, has no capacity cap. (Before version 0.2.0 the capacity was applied before the aggregate deductible, which gave smaller ceded totals when the two were combined.)

Totals are returned at full precision; round them only for display.

Random numbers: each chunk of simulations uses its own L'Ecuyer-CMRG random stream, derived from one seed, so a run gives the same results whether or not it runs in parallel. With seedSetBinary = TRUE (the default when a seedValue is given) the run is reproducible from seedValue and the caller's random number stream is left unchanged; otherwise the seed is drawn from the caller's stream, so set.seed() before the call also makes it reproducible. The streams always use Inversion for normal draws and Rejection sampling, so a seed gives the same results whatever the caller's RNGkind(), which is restored afterwards. Results depend on the chunk size, which by default adapts to the expected number of claims per simulation.

Value

A data frame with one row per simulation, at full precision: claim_counts, the claim count; total_claims, the total claims after the reinsurance structures; gross_claims, the gross total claims before them (after Pareto slices and the severity cap; unless gross = FALSE); and, when reinstatements are limited, number_of_reinstatements_used: the EEL layer's recoveries in the period divided by the EEL limit, capped at the number of reinstatements, so reinstatements are counted pro rata to the amount recovered. The recoveries are taken after the aggregate deductible and limit of an aggregate 'Unlimited Layer' or 'Limited Layer', but before an aggregate 'Exclude Layer' is taken out: with an exclusion they are the EEL recoveries after the reinstatement capacity. For example, three claims of 100 through a layer of 60 excess of 30 with two reinstatements and an aggregate exclusion of 150 excess of 50 give a total of 50 but 2 reinstatements used (180 / 60, capped at 2). Stops with an error that names any required setting that is missing or invalid.

See Also

simulate_claims, a simpler interface with short argument names, and run_shiny_simulator for the same model in an app.

Examples

# 1,000 simulated years of Poisson claim counts with Normal claim sizes, no reinsurance
results <- simulate_function(
  numOfSimulations = 1000, freq_params = 3, sev_params = c(1000, 200),
  seedSetBinary = TRUE, seedValue = 1, freqDistr = "Poisson", sevDistr = "Normal"
)
summary(results$total_claims)

# the same claims ceded to a layer of 1,500 excess of 800 on each claim
layer <- simulate_function(
  numOfSimulations = 1000, freq_params = 3, sev_params = c(1000, 200),
  seedSetBinary = TRUE, seedValue = 1, freqDistr = "Poisson", sevDistr = "Normal",
  reinsuranceStructureEEL = "Limited Layer",
  reinsurance_structure_eel_dedctible_amount = 800,
  reinsurance_structure_eel_limit_amount = 1500
)
mean(layer$total_claims)