Actuarial functions and heavy tailed distributions for R
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README.md

actuar

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actuar is a package providing additional actuarial science functionality to the R statistical system. The project was officially launched in 2005 and is under active development.

Features

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

  1. Additional probability distributions to model insurance loss amounts and loss frequency (19 continuous heavy tailed distributions, see the list below; the Poisson-inverse Gaussian discrete distribution; zero-truncated and zero-modified extensions of the standard discrete distributions; phase-type distributions);
  2. Loss distributions modeling (extensive support for grouped data; empirical raw and limited moments; minimum distance estimation);
  3. Risk and ruin theory (discretization of the claim amount distribution and computation of the aggregate claim amount distribution; computation of the adjustment coefficient and ruin probabilities);
  4. Simulation of discrete mixtures, compound models and compound hierarchical models;
  5. Credibility theory (Bühlmann, Bühlmann-Straub, hierarchical, regression and linear Bayes models).

The package includes extensive documentation in the form of package vignettes. Each vignette focuses on a feature set of the package. To get the list of available vignettes, enter at the R command prompt:

vignette(package = "actuar")

Installation

You should install the stable version of the package from the Comprehensive R Archive Network (CRAN): using:

install.packages("actuar")

Citation

To cite package actuar in publications see the output of

citation(package = "actuar")

License

actuar is free software licensed under the GNU General Public License (GPL), version 2 or later.

Philosophy

As much as possible, the developers have tried to keep the user interface of the various functions of the package consistent. Moreover, the package follows the general R philosophy of working with model objects. This means that instead of merely returning, say, a vector of probabilities, many functions will return an object containing, among other things, the said probabilities. The object can then be manipulated at one's will using various extraction, summary or plotting functions.

Additional continuous distributions

actuar provides support functions for all the probability distributions found in Appendix A of Loss Models: From Data to Decisions, 4th Edition and not already present in base R, excluding the log-t, but including the loggamma distribution. These distributions mostly fall under the umbrella of extreme value or heavy tailed distributions.

The list of distributions supported by actuar is as follows, using the nomenclature of Loss Models.

Transformed beta family

  • Transformed beta
  • Burr
  • Loglogistic
  • Paralogistic
  • Generalized Pareto
  • Pareto
  • Inverse Burr
  • Inverse Pareto
  • Inverse paralogistic

Transformed gamma family

  • Transformed gamma
  • Inverse transformed gamma
  • Inverse gamma
  • Inverse Weibull
  • Inverse exponential

Other

  • Loggamma
  • Gumbel
  • Inverse Gaussian
  • Single parameter Pareto
  • Generalized beta