# Actuarial Functions and Heavy Tailed Distributions

## Documentation for package ‘actuar’ version 3.0-0

- DESCRIPTION file.
- User guides, package vignettes and other documentation.
- Code demos. Use demo() to run them.
- Package NEWS.

## Help Pages

A B C D E F G H I K L M N O P Q R S T U V W Z misc

## -- A --

adjCoef | Adjustment Coefficient
aggregate.portfolio | Summary Statistics of a Portfolio
aggregateDist | Aggregate Claim Amount Distribution

## -- B --

betaint | The "Beta Integral"
BetaMoments | Raw and Limited Moments of the Beta Distribution
Burr | The Burr Distribution

## -- C --

ChisqSupp | Moments and Moment Generating Function of the (non-central) Chi-Squared Distribution
cm | Credibility Models
Coverage | Density and Cumulative Distribution Function for Modified Data
coverage | Density and Cumulative Distribution Function for Modified Data
CTE | Conditional Tail Expectation
CTE.aggregateDist | Conditional Tail Expectation

## -- D --

dburr | The Burr Distribution
dental | Individual Dental Claims Data Set
dfpareto | The Feller Pareto Distribution
dgenbeta | The Generalized Beta Distribution
dgenpareto | The Generalized Pareto Distribution
dgumbel | The Gumbel Distribution
diff.aggregateDist | Aggregate Claim Amount Distribution
dinvburr | The Inverse Burr Distribution
dinvexp | The Inverse Exponential Distribution
dinvgamma | The Inverse Gamma Distribution
dinvgauss | The Inverse Gaussian Distribution
dinvparalogis | The Inverse Paralogistic Distribution
dinvpareto | The Inverse Pareto Distribution
dinvtrgamma | The Inverse Transformed Gamma Distribution
dinvweibull | The Inverse Weibull Distribution
discretise | Discretization of a Continuous Distribution
discretize | Discretization of a Continuous Distribution
dlgamma | The Loggamma Distribution
dlgompertz | The Inverse Weibull Distribution
dllogis | The Loglogistic Distribution
dlogarithmic | The Logarithmic Distribution
dparalogis | The Paralogistic Distribution
dpareto | The Pareto Distribution
dpareto1 | The Single-parameter Pareto Distribution
dpareto2 | The Pareto II Distribution
dpareto3 | The Pareto III Distribution
dpareto4 | The Pareto IV Distribution
dpearson6 | The Transformed Beta Distribution
dphtype | The Phase-type Distribution
dpig | The Poisson-Inverse Gaussian Distribution
dpoisinvgauss | The Poisson-Inverse Gaussian Distribution
dtrbeta | The Transformed Beta Distribution
dtrgamma | The Transformed Gamma Distribution
dzmbinom | The Zero-Modified Binomial Distribution
dzmgeom | The Zero-Modified Geometric Distribution
dzmlogarithmic | The Zero-Modified Logarithmic Distribution
dzmnbinom | The Zero-Modified Negative Binomial Distribution
dzmpois | The Zero-Modified Poisson Distribution
dztbinom | The Zero-Truncated Binomial Distribution
dztgeom | The Zero-Truncated Geometric Distribution
dztnbinom | The Zero-Truncated Negative Binomial Distribution
dztpois | The Zero-Truncated Poisson Distribution

## -- E --

elev | Empirical Limited Expected Value
elev.default | Empirical Limited Expected Value
elev.grouped.data | Empirical Limited Expected Value
emm | Empirical Moments
emm.default | Empirical Moments
emm.grouped.data | Empirical Moments
ExponentialSupp | Moments and Moment Generating Function of the Exponential Distribution
Extract.grouped.data | Extract or Replace Parts of a Grouped Data Object

## -- F --

FellerPareto | The Feller Pareto Distribution
frequency.portfolio | Summary Statistics of a Portfolio

## -- G --

GammaSupp | Moments and Moment Generating Function of the Gamma Distribution
gdental | Grouped Dental Claims Data Set
GeneralizedBeta | The Generalized Beta Distribution
GeneralizedPareto | The Generalized Pareto Distribution
grouped.data | Grouped data
Gumbel | The Gumbel Distribution

## -- H --

hachemeister | Hachemeister Data Set
hist.grouped.data | Histogram for Grouped Data

## -- I --

InverseBurr | The Inverse Burr Distribution
InverseExponential | The Inverse Exponential Distribution
InverseGamma | The Inverse Gamma Distribution
InverseGaussian | The Inverse Gaussian Distribution
InverseParalogistic | The Inverse Paralogistic Distribution
InversePareto | The Inverse Pareto Distribution
InverseTransformedGamma | The Inverse Transformed Gamma Distribution
InverseWeibull | The Inverse Weibull Distribution

## -- K --

knots.elev | Empirical Limited Expected Value
knots.ogive | Ogive for Grouped Data

## -- L --

levbeta | Raw and Limited Moments of the Beta Distribution
levburr | The Burr Distribution
levchisq | Moments and Moment Generating Function of the (non-central) Chi-Squared Distribution
levexp | Moments and Moment Generating Function of the Exponential Distribution
levfpareto | The Feller Pareto Distribution
levgamma | Moments and Moment Generating Function of the Gamma Distribution
levgenbeta | The Generalized Beta Distribution
levgenpareto | The Generalized Pareto Distribution
levinvburr | The Inverse Burr Distribution
levinvexp | The Inverse Exponential Distribution
levinvgamma | The Inverse Gamma Distribution
levinvgauss | The Inverse Gaussian Distribution
levinvparalogis | The Inverse Paralogistic Distribution
levinvpareto | The Inverse Pareto Distribution
levinvtrgamma | The Inverse Transformed Gamma Distribution
levinvweibull | The Inverse Weibull Distribution
levlgamma | The Loggamma Distribution
levlgompertz | The Inverse Weibull Distribution
levllogis | The Loglogistic Distribution
levlnorm | Raw and Limited Moments of the Lognormal Distribution
levparalogis | The Paralogistic Distribution
levpareto | The Pareto Distribution
levpareto1 | The Single-parameter Pareto Distribution
levpareto2 | The Pareto II Distribution
levpareto3 | The Pareto III Distribution
levpareto4 | The Pareto IV Distribution
levpearson6 | The Transformed Beta Distribution
levtrbeta | The Transformed Beta Distribution
levtrgamma | The Transformed Gamma Distribution
levunif | Moments and Moment Generating Function of the Uniform Distribution
levweibull | Raw and Limited Moments of the Weibull Distribution
log-series | The Logarithmic Distribution
Logarithmic | The Logarithmic Distribution
Loggamma | The Loggamma Distribution
Loglogistic | The Loglogistic Distribution
LognormalMoments | Raw and Limited Moments of the Lognormal Distribution

## -- M --

mbeta | Raw and Limited Moments of the Beta Distribution
mburr | The Burr Distribution
mchisq | Moments and Moment Generating Function of the (non-central) Chi-Squared Distribution
Mde | Minimum Distance Estimation
mde | Minimum Distance Estimation
mean.aggregateDist | Aggregate Claim Amount Distribution
mean.grouped.data | Arithmetic Mean
mexp | Moments and Moment Generating Function of the Exponential Distribution
mfpareto | The Feller Pareto Distribution
mgamma | Moments and Moment Generating Function of the Gamma Distribution
mgenbeta | The Generalized Beta Distribution
mgenpareto | The Generalized Pareto Distribution
mgfchisq | Moments and Moment Generating Function of the (non-central) Chi-Squared Distribution
mgfexp | Moments and Moment Generating Function of the Exponential Distribution
mgfgamma | Moments and Moment Generating Function of the Gamma Distribution
mgfgumbel | The Gumbel Distribution
mgfinvgamma | The Inverse Gamma Distribution
mgfinvgauss | The Inverse Gaussian Distribution
mgfnorm | Moments and Moment generating function of the Normal Distribution
mgfphtype | The Phase-type Distribution
mgfunif | Moments and Moment Generating Function of the Uniform Distribution
mgumbel | The Gumbel Distribution
minvburr | The Inverse Burr Distribution
minvexp | The Inverse Exponential Distribution
minvgamma | The Inverse Gamma Distribution
minvgauss | The Inverse Gaussian Distribution
minvparalogis | The Inverse Paralogistic Distribution
minvpareto | The Inverse Pareto Distribution
minvtrgamma | The Inverse Transformed Gamma Distribution
minvweibull | The Inverse Weibull Distribution
mlgamma | The Loggamma Distribution
mlgompertz | The Inverse Weibull Distribution
mllogis | The Loglogistic Distribution
mlnorm | Raw and Limited Moments of the Lognormal Distribution
mnorm | Moments and Moment generating function of the Normal Distribution
mparalogis | The Paralogistic Distribution
mpareto | The Pareto Distribution
mpareto1 | The Single-parameter Pareto Distribution
mpareto2 | The Pareto II Distribution
mpareto3 | The Pareto III Distribution
mpareto4 | The Pareto IV Distribution
mpearson6 | The Transformed Beta Distribution
mphtype | The Phase-type Distribution
mtrbeta | The Transformed Beta Distribution
mtrgamma | The Transformed Gamma Distribution
munif | Moments and Moment Generating Function of the Uniform Distribution
mweibull | Raw and Limited Moments of the Weibull Distribution

## -- N --

NormalSupp | Moments and Moment generating function of the Normal Distribution

## -- O --

ogive | Ogive for Grouped Data
ogive.default | Ogive for Grouped Data
ogive.grouped.data | Ogive for Grouped Data

## -- P --

Paralogistic | The Paralogistic Distribution
Pareto | The Pareto Distribution
Pareto2 | The Pareto II Distribution
Pareto3 | The Pareto III Distribution
Pareto4 | The Pareto IV Distribution
pburr | The Burr Distribution
Pearson6 | The Transformed Beta Distribution
pfpareto | The Feller Pareto Distribution
pgenbeta | The Generalized Beta Distribution
pgenpareto | The Generalized Pareto Distribution
pgumbel | The Gumbel Distribution
PIG | The Poisson-Inverse Gaussian Distribution
pinvburr | The Inverse Burr Distribution
pinvexp | The Inverse Exponential Distribution
pinvgamma | The Inverse Gamma Distribution
pinvgauss | The Inverse Gaussian Distribution
pinvparalogis | The Inverse Paralogistic Distribution
pinvpareto | The Inverse Pareto Distribution
pinvtrgamma | The Inverse Transformed Gamma Distribution
pinvweibull | The Inverse Weibull Distribution
plgamma | The Loggamma Distribution
plgompertz | The Inverse Weibull Distribution
pllogis | The Loglogistic Distribution
plogarithmic | The Logarithmic Distribution
plot.adjCoef | Adjustment Coefficient
plot.aggregateDist | Aggregate Claim Amount Distribution
plot.elev | Empirical Limited Expected Value
plot.ogive | Ogive for Grouped Data
plot.ruin | Probability of Ruin
PoissonInverseGaussian | The Poisson-Inverse Gaussian Distribution
pparalogis | The Paralogistic Distribution
ppareto | The Pareto Distribution
ppareto1 | The Single-parameter Pareto Distribution
ppareto2 | The Pareto II Distribution
ppareto3 | The Pareto III Distribution
ppareto4 | The Pareto IV Distribution
ppearson6 | The Transformed Beta Distribution
pphtype | The Phase-type Distribution
ppig | The Poisson-Inverse Gaussian Distribution
ppoisinvgauss | The Poisson-Inverse Gaussian Distribution
predict.cm | Credibility Models
print.aggregateDist | Aggregate Claim Amount Distribution
print.cm | Credibility Models
print.elev | Empirical Limited Expected Value
print.ogive | Ogive for Grouped Data
print.portfolio | Simulation from Compound Hierarchical Models
print.summary.cm | Credibility Models
ptrbeta | The Transformed Beta Distribution
ptrgamma | The Transformed Gamma Distribution
pzmbinom | The Zero-Modified Binomial Distribution
pzmgeom | The Zero-Modified Geometric Distribution
pzmlogarithmic | The Zero-Modified Logarithmic Distribution
pzmnbinom | The Zero-Modified Negative Binomial Distribution
pzmpois | The Zero-Modified Poisson Distribution
pztbinom | The Zero-Truncated Binomial Distribution
pztgeom | The Zero-Truncated Geometric Distribution
pztnbinom | The Zero-Truncated Negative Binomial Distribution
pztpois | The Zero-Truncated Poisson Distribution

## -- Q --

qburr | The Burr Distribution
qfpareto | The Feller Pareto Distribution
qgenbeta | The Generalized Beta Distribution
qgenpareto | The Generalized Pareto Distribution
qgumbel | The Gumbel Distribution
qinvburr | The Inverse Burr Distribution
qinvexp | The Inverse Exponential Distribution
qinvgamma | The Inverse Gamma Distribution
qinvgauss | The Inverse Gaussian Distribution
qinvparalogis | The Inverse Paralogistic Distribution
qinvpareto | The Inverse Pareto Distribution
qinvtrgamma | The Inverse Transformed Gamma Distribution
qinvweibull | The Inverse Weibull Distribution
qlgamma | The Loggamma Distribution
qlgompertz | The Inverse Weibull Distribution
qllogis | The Loglogistic Distribution
qlogarithmic | The Logarithmic Distribution
qparalogis | The Paralogistic Distribution
qpareto | The Pareto Distribution
qpareto1 | The Single-parameter Pareto Distribution
qpareto2 | The Pareto II Distribution
qpareto3 | The Pareto III Distribution
qpareto4 | The Pareto IV Distribution
qpearson6 | The Transformed Beta Distribution
qpig | The Poisson-Inverse Gaussian Distribution
qpoisinvgauss | The Poisson-Inverse Gaussian Distribution
qtrbeta | The Transformed Beta Distribution
qtrgamma | The Transformed Gamma Distribution
quantile.aggregateDist | Quantiles of Aggregate Claim Amount Distribution
quantile.grouped.data | Quantiles of Grouped Data
qzmbinom | The Zero-Modified Binomial Distribution
qzmgeom | The Zero-Modified Geometric Distribution
qzmlogarithmic | The Zero-Modified Logarithmic Distribution
qzmnbinom | The Zero-Modified Negative Binomial Distribution
qzmpois | The Zero-Modified Poisson Distribution
qztbinom | The Zero-Truncated Binomial Distribution
qztgeom | The Zero-Truncated Geometric Distribution
qztnbinom | The Zero-Truncated Negative Binomial Distribution
qztpois | The Zero-Truncated Poisson Distribution

## -- R --

rburr | The Burr Distribution
rcomphierarc | Simulation from Compound Hierarchical Models
rcomphierarc.summaries | Summary Statistics of a Portfolio
rcompound | Simulation from Compound Models
rcomppois | Simulation from Compound Models
rfpareto | The Feller Pareto Distribution
rgenbeta | The Generalized Beta Distribution
rgenpareto | The Generalized Pareto Distribution
rgumbel | The Gumbel Distribution
rinvburr | The Inverse Burr Distribution
rinvexp | The Inverse Exponential Distribution
rinvgamma | The Inverse Gamma Distribution
rinvgauss | The Inverse Gaussian Distribution
rinvparalogis | The Inverse Paralogistic Distribution
rinvpareto | The Inverse Pareto Distribution
rinvtrgamma | The Inverse Transformed Gamma Distribution
rinvweibull | The Inverse Weibull Distribution
rlgamma | The Loggamma Distribution
rlgompertz | The Inverse Weibull Distribution
rllogis | The Loglogistic Distribution
rlogarithmic | The Logarithmic Distribution
rmixture | Simulation from Discrete Mixtures
rparalogis | The Paralogistic Distribution
rpareto | The Pareto Distribution
rpareto1 | The Single-parameter Pareto Distribution
rpareto2 | The Pareto II Distribution
rpareto3 | The Pareto III Distribution
rpareto4 | The Pareto IV Distribution
rpearson6 | The Transformed Beta Distribution
rphtype | The Phase-type Distribution
rpig | The Poisson-Inverse Gaussian Distribution
rpoisinvgauss | The Poisson-Inverse Gaussian Distribution
rtrbeta | The Transformed Beta Distribution
rtrgamma | The Transformed Gamma Distribution
ruin | Probability of Ruin
rzmbinom | The Zero-Modified Binomial Distribution
rzmgeom | The Zero-Modified Geometric Distribution
rzmlogarithmic | The Zero-Modified Logarithmic Distribution
rzmnbinom | The Zero-Modified Negative Binomial Distribution
rzmpois | The Zero-Modified Poisson Distribution
rztbinom | The Zero-Truncated Binomial Distribution
rztgeom | The Zero-Truncated Geometric Distribution
rztnbinom | The Zero-Truncated Negative Binomial Distribution
rztpois | The Zero-Truncated Poisson Distribution

## -- S --

severity | Manipulation of Individual Claim Amounts
severity.default | Manipulation of Individual Claim Amounts
severity.portfolio | Summary Statistics of a Portfolio
simpf | Simulation from Compound Hierarchical Models
simul | Simulation from Compound Hierarchical Models
simul.summaries | Summary Statistics of a Portfolio
SingleParameterPareto | The Single-parameter Pareto Distribution
summary.aggregateDist | Aggregate Claim Amount Distribution
summary.cm | Credibility Models
summary.elev | Empirical Limited Expected Value
summary.ogive | Ogive for Grouped Data

## -- T --

TransformedBeta | The Transformed Beta Distribution
TransformedGamma | The Transformed Gamma Distribution
TVaR | Conditional Tail Expectation

## -- U --

UniformSupp | Moments and Moment Generating Function of the Uniform Distribution
unroll | Display a Two-Dimension Version of a Matrix of Vectors

## -- V --

VaR | Value at Risk
VaR.aggregateDist | Quantiles of Aggregate Claim Amount Distribution

## -- W --

WeibullMoments | Raw and Limited Moments of the Weibull Distribution
weights.portfolio | Summary Statistics of a Portfolio

## -- Z --

ZeroModifiedBinomial | The Zero-Modified Binomial Distribution
ZeroModifiedGeometric | The Zero-Modified Geometric Distribution
ZeroModifiedLogarithmic | The Zero-Modified Logarithmic Distribution
ZeroModifiedNegativeBinomial | The Zero-Modified Negative Binomial Distribution
ZeroModifiedPoisson | The Zero-Modified Poisson Distribution
ZeroTruncatedBinomial | The Zero-Truncated Binomial Distribution
ZeroTruncatedGeometric | The Zero-Truncated Geometric Distribution
ZeroTruncatedNegativeBinomial | The Zero-Truncated Negative Binomial Distribution
ZeroTruncatedPoisson | The Zero-Truncated Poisson Distribution
ZMBinomial | The Zero-Modified Binomial Distribution
Zmgeometric | The Zero-Modified Geometric Distribution
ZMLogarithmic | The Zero-Modified Logarithmic Distribution
ZMNegativeBinomial | The Zero-Modified Negative Binomial Distribution
ZMNegBinomial | The Zero-Modified Negative Binomial Distribution
ZMpoisson | The Zero-Modified Poisson Distribution
ZTBinomial | The Zero-Truncated Binomial Distribution
ZTGeometric | The Zero-Truncated Geometric Distribution
ZTNegativeBinomial | The Zero-Truncated Negative Binomial Distribution
ZTNegBinomial | The Zero-Truncated Negative Binomial Distribution
ZTPoisson | The Zero-Truncated Poisson Distribution

## -- misc --

[.grouped.data | Extract or Replace Parts of a Grouped Data Object
[<-.grouped.data | Extract or Replace Parts of a Grouped Data Object