actuar-package: Actuarial Functions and Heavy Tailed Distributions

In actuar: Actuarial Functions and Heavy Tailed Distributions

Actuarial Functions and Heavy Tailed Distributions

Description

Functions and data sets for actuarial science: modeling of loss distributions; risk theory and ruin theory; simulation of compound models, discrete mixtures and compound hierarchical models; credibility theory. Support for many additional probability distributions to model insurance loss size and frequency: 23 continuous heavy tailed distributions; the Poisson-inverse Gaussian discrete distribution; zero-truncated and zero-modified extensions of the standard discrete distributions. Support for phase-type distributions commonly used to compute ruin probabilities. Main reference: <doi:10.18637/jss.v025.i07>. Implementation of the Feller-Pareto family of distributions: <doi:10.18637/jss.v103.i06>.

Details

actuar provides additional actuarial science functionality and support for heavy tailed distributions to the R statistical system.

The current feature set of the package can be split into five main categories.

1. Additional probability distributions: 23 continuous heavy tailed distributions from the Feller-Pareto and Transformed Gamma families, the loggamma, the Gumbel, the inverse Gaussian and the generalized beta; phase-type distributions; the Poisson-inverse Gaussian discrete distribution; zero-truncated and zero-modified extensions of the standard discrete distributions; computation of raw moments, limited moments and the moment generating function (when it exists) of continuous distributions. See the “distributions” package vignette for details.

2. Loss distributions modeling: extensive support of grouped data; functions to compute empirical raw and limited moments; support for minimum distance estimation using three different measures; treatment of coverage modifications (deductibles, limits, inflation, coinsurance). See the “modeling” and “coverage” package vignettes for details.

3. Risk and ruin theory: discretization of the claim amount distribution; calculation of the aggregate claim amount distribution; calculation of the adjustment coefficient; calculation of the probability of ruin, including using phase-type distributions. See the “risk” package vignette for details.

4. Simulation of discrete mixtures, compound models (including the compound Poisson), and compound hierarchical models. See the “simulation” package vignette for details.

5. Credibility theory: function cm fits hierarchical (including Bühlmann, Bühlmann-Straub), regression and linear Bayes credibility models. See the “credibility” package vignette for details.

Author(s)

Christophe Dutang, Vincent Goulet, Mathieu Pigeon and many other contributors; use packageDescription("actuar") for the complete list.

Maintainer: Vincent Goulet.

References

Dutang, C., Goulet, V. and Pigeon, M. (2008). actuar: An R Package for Actuarial Science. Journal of Statistical Software, 25(7), 1–37. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v025.i07")}.

Dutang, C., Goulet, V., Langevin, N. (2022). Feller-Pareto and Related Distributions: Numerical Implementation and Actuarial Applications. Journal of Statistical Software, 103(6), 1–22. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v103.i06")}.

Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2012), Loss Models, From Data to Decisions, Fourth Edition, Wiley.

See Also

For probability distributions support functions, use as starting points: FellerPareto, TransformedGamma, Loggamma, Gumbel, InverseGaussian, PhaseType, PoissonInverseGaussian and, e.g., ZeroTruncatedPoisson, ZeroModifiedPoisson.

For loss modeling support functions: grouped.data, ogive, emm, elev, mde, coverage.

For risk and ruin theory functions: discretize, aggregateDist, adjCoef, ruin.

For credibility theory functions and datasets: cm, hachemeister.

Examples

## The package comes with extensive demonstration scripts;
## use the following command to obtain the list.
## Not run: demo(package = "actuar")

actuar documentation built on Nov. 8, 2023, 9:06 a.m.