# Functions from "Reinsurance: Actuarial and Statistical Aspects"

## Documentation for package ‘ReIns’ version 1.0.15

- DESCRIPTION file.
- User guides, package vignettes and other documentation.
- Package NEWS.

## Help Pages

C D E G H I K L M N P Q R S T V W

## -- C --

cEPD | EPD estimator for right censored data
cExpQQ | Exponential quantile plot for right censored data
cgenHill | Generalised Hill estimator for right censored data
cGPDmle | GPD-ML estimator for right censored data
cHill | Hill estimator for right censored data
cLognormalQQ | Log-normal quantile plot for right censored data
cMoment | MOM estimator for right censored data
cParetoQQ | Pareto quantile plot for right censored data
cPOT | GPD-ML estimator for right censored data
cProb | Estimator of small exceedance probabilities and large return periods using censored Hill
cProbEPD | Estimator of small exceedance probabilities and large return periods using censored EPD
cProbGH | Estimator of small exceedance probabilities and large return periods using censored generalised Hill
cProbGPD | Estimator of small exceedance probabilities and large return periods using censored GPD-MLE
cProbMOM | Estimator of small exceedance probabilities and large return periods using censored MOM
cQuant | Estimator of large quantiles using censored Hill
cQuantGH | Estimator of large quantiles using censored Hill
cQuantGPD | Estimator of large quantiles using censored GPD-MLE
cQuantMOM | Estimator of large quantiles using censored MOM
cReturn | Estimator of small exceedance probabilities and large return periods using censored Hill
cReturnEPD | Estimator of small exceedance probabilities and large return periods using censored EPD
cReturnGH | Estimator of small exceedance probabilities and large return periods using censored generalised Hill
cReturnGPD | Estimator of small exceedance probabilities and large return periods using censored GPD-MLE
cReturnMOM | Estimator of small exceedance probabilities and large return periods using censored MOM
crHill | Hill-type estimator for the conditional EVI
crParetoQQ | Conditional Pareto quantile plot for right censored data
crSurv | Non-parametric estimator of conditional survival function
CTE | Conditional Tail Expectation
cWeibullQQ | Weibull quantile plot for right censored data

## -- D --

dburr | The Burr distribution
depd | The Extended Pareto Distribution
dfrechet | The Frechet distribution
dgpd | The generalised Pareto distribution
dpareto | The Pareto distribution
dSplice | Spliced distribution
dtburr | The truncated Burr distribution
dtexp | The truncated exponential distribution
dtfrechet | The truncated Frechet distribution
dtgpd | The truncated generalised Pareto distribution
dtlnorm | The truncated log-normal distribution
dtpareto | The truncated Pareto distribution
dtweibull | The truncated Weibull distribution

## -- E --

EPD | EPD estimator
EPDfit | Fit EPD using MLE
ES | Conditional Tail Expectation
EVTfit | EVT fit
ExcessEPD | Estimates for excess-loss premiums using EPD estimates
ExcessGPD | Estimates for excess-loss premiums using GPD-MLE estimates
ExcessHill | Estimates for excess-loss premiums using a Pareto model
ExcessPareto | Estimates for excess-loss premiums using a Pareto model
ExcessSplice | Estimates for excess-loss premiums using splicing
ExpQQ | Exponential quantile plot

## -- G --

generalizedQQ | Generalised quantile plot
genHill | Generalised Hill estimator
genQQ | Generalised quantile plot
GPDfit | Fit GPD using MLE
GPDmle | GPD-ML estimator
GPDresiduals | GPD residual plot

## -- H --

Hill | Hill estimator
Hill.2oQV | Bias-reduced MLE (Quantile view)
Hill.kopt | Select optimal threshold for Hill estimator

## -- I --

icHill | Hill estimator for interval censored data
icParetoQQ | Pareto quantile plot for interval censored data

## -- K --

KaplanMeier | Kaplan-Meier estimator

## -- L --

LognormalQQ | Log-normal quantile plot
LognormalQQ_der | Derivative plot of the log-normal QQ-plot
LStail | Least Squares tail estimator

## -- M --

MeanExcess | Mean excess function
MeanExcess_TB | Mean excess function using Turnbull estimator
MEfit | Mixed Erlang fit
Moment | Moment estimator

## -- N --

norwegianfire | Norwegian fire insurance data

## -- P --

ParetoQQ | Pareto quantile plot
ParetoQQ_der | Derivative plot of the Pareto QQ-plot
pburr | The Burr distribution
pClas | Classical estimators for the CDF
pEdge | Edgeworth approximation
pepd | The Extended Pareto Distribution
pfrechet | The Frechet distribution
pGC | Gram-Charlier approximation
pgpd | The generalised Pareto distribution
POT | GPD-ML estimator
ppareto | The Pareto distribution
Prob | Weissman estimator of small exceedance probabilities and large return periods
ProbEPD | Estimator of small exceedance probabilities and large return periods using EPD
ProbGH | Estimator of small exceedance probabilities and large return periods using generalised Hill
ProbGPD | Estimator of small exceedance probabilities and large return periods using GPD-MLE
ProbMOM | Estimator of small exceedance probabilities and large return periods using MOM
ProbReg | Estimator of small tail probability in regression
pSplice | Spliced distribution
ptburr | The truncated Burr distribution
ptexp | The truncated exponential distribution
ptfrechet | The truncated Frechet distribution
ptgpd | The truncated generalised Pareto distribution
ptlnorm | The truncated log-normal distribution
ptpareto | The truncated Pareto distribution
ptweibull | The truncated Weibull distribution

## -- Q --

qburr | The Burr distribution
qepd | The Extended Pareto Distribution
qfrechet | The Frechet distribution
qgpd | The generalised Pareto distribution
qpareto | The Pareto distribution
qSplice | Spliced distribution
qtburr | The truncated Burr distribution
qtexp | The truncated exponential distribution
qtfrechet | The truncated Frechet distribution
qtgpd | The truncated generalised Pareto distribution
qtlnorm | The truncated log-normal distribution
qtpareto | The truncated Pareto distribution
qtweibull | The truncated Weibull distribution
Quant | Weissman estimator of extreme quantiles
Quant.2oQV | Second order refined Weissman estimator of extreme quantiles (QV)
QuantGH | Estimator of extreme quantiles using generalised Hill
QuantGPD | Estimator of extreme quantiles using GPD-MLE
QuantMOM | Estimator of extreme quantiles using MOM
QuantReg | Estimator of extreme quantiles in regression

## -- R --

rburr | The Burr distribution
repd | The Extended Pareto Distribution
Return | Weissman estimator of small exceedance probabilities and large return periods
ReturnEPD | Estimator of small exceedance probabilities and large return periods using EPD
ReturnGH | Estimator of small exceedance probabilities and large return periods using generalised Hill
ReturnGPD | Estimator of small exceedance probabilities and large return periods using GPD-MLE
ReturnMOM | Estimator of small exceedance probabilities and large return periods using MOM
rfrechet | The Frechet distribution
rgpd | The generalised Pareto distribution
rpareto | The Pareto distribution
rSplice | Spliced distribution
rtburr | The truncated Burr distribution
rtexp | The truncated exponential distribution
rtfrechet | The truncated Frechet distribution
rtgpd | The truncated generalised Pareto distribution
rtlnorm | The truncated log-normal distribution
rtpareto | The truncated Pareto distribution
rtweibull | The truncated Weibull distribution

## -- S --

Scale | Scale estimator
Scale.2o | Bias-reduced scale estimator using second order Hill estimator
ScaleEPD | Bias-reduced scale estimator using EPD estimator
ScaleReg | Scale estimator in regression
secura | Secura dataset
soa | SOA Group Medical Insurance Large Claims Database
SpliceECDF | Plot of fitted and empirical survival function
SpliceFit | Splicing fit
SpliceFitGPD | Splicing of mixed Erlang and GPD using POT-MLE
SpliceFitHill | Splicing of mixed Erlang and Pareto
SpliceFiticPareto | Splicing of mixed Erlang and Pareto for interval censored data
SpliceFitPareto | Splicing of mixed Erlang and Pareto
SpliceLL | LL-plot with fitted and empirical survival function
SpliceLL_TB | LL-plot with fitted and Turnbull survival function
SplicePP | PP-plot with fitted and empirical survival function
SplicePP_TB | PP-plot with fitted and Turnbull survival function
SpliceQQ | Splicing quantile plot
SpliceQQ_TB | Splicing quantile plot using Turnbull estimator
SpliceTB | Plot of fitted and Turnbull survival function
stdf | Non-parametric estimators of the STDF
stdf2 | Non-parametric estimators of the STDF

## -- T --

trDT | Truncation odds
trDTMLE | Truncation odds
trEndpoint | Estimator of endpoint
trEndpointMLE | Estimator of endpoint
trHill | Hill estimator for upper truncated data
trMLE | MLE estimator for upper truncated data
trParetoQQ | Truncated Pareto quantile plot
trProb | Estimator of small exceedance probabilities using truncated Hill
trProbMLE | Estimator of small exceedance probabilities using truncated MLE
trQuant | Estimator of large quantiles using truncated Hill
trQuantMLE | Estimator of large quantiles using truncated MLE
trQuantW | Estimator of large quantiles using truncated Hill
trTest | Test for truncated Pareto-type tails
trTestMLE | Test for truncated GPD tails
TSfraction | Least Squares tail estimator
Turnbull | Turnbull estimator

## -- V --

VaR | VaR of splicing fit

## -- W --

WeibullQQ | Weibull quantile plot
WeibullQQ_der | Derivative plot of the Weibull QQ-plot
Weissman.p | Weissman estimator of small exceedance probabilities and large return periods
Weissman.q | Weissman estimator of extreme quantiles
Weissman.q.2oQV | Second order refined Weissman estimator of extreme quantiles (QV)
Weissman.r | Weissman estimator of small exceedance probabilities and large return periods