tvarPackage

To download this R package on your R session, copy-paste the next code line (the package devtools is necessary) :

devtools::install_github("gabrielcrepeault/tvarPackage")

Introduction

This R package was created in the first place to calculate more quickly and easily a lot of formulas (mean, variance, VaR, TVaR, stop-loss function, etc.) related to popular probability distributions, such as :

  • Uniform
  • Binomial
  • Poisson
  • Exponential
  • Gamma
  • Pareto
  • Beta
  • Lognormal
  • Pareto
  • Normal

And also some Mortality laws, like

  • Gompertz

Formulas convention

I’ve tried to make the package pretty simple to use, the syntax is based on quite the same as some popular R package, like the stats or actuar packages :

Formulas code
Mean E_<distribution>
Variance V_<distribution>
stop loss SL_<distribution>
Limited expected value Elim_<distribution>
truncated mean Etronq_<distribution>
Value-at-Risk VaR_<distribution>
Tail Value-at-Risk TVaR_<distribution>
Mean Excess-loss Mexcess_<distribution>

Specifications for Life insurance

For probability laws used in life insurance, there is a special annotation (not much different from the one above) :

  • first, you need to specify if you want to have the probability related to $X$ or $T_x$ (Tx = T si setup by default)
  • The Mean, Variance, VaR and TVaR expressions are given as a result of the integrate function or with floor equivalent, because there are no closed (explicit) expressions. You can call them with a slightly different syntax, Etx_<distribution>, Vtx_<distribution> and TVaRtx_<distribution>.
  • In life insurance , we work with survival functions most of the time. So I have also defined a survival function (it’s gonna save coding time and space). As the section above, the syntax is based on what’s already in the most popular packages.
  • There is less practical application for VaR and TVaR for life duration, so I didn’t create VaR functions, since the quantilee fonction makes more sense.
Formulas code
Mortality force h<distribution>
density function d<distribution>
cumulative density function (cdf) p<distribution>
survival function (cdf) s<distribution>

Updates

Date Modifications
24/02/2018 Intial commit of the package
27/02/2018 adding binomial, uniform and exponential laws
04/03/2018 adding beta distribution
06/03/2018 adding Lognormal distribution
06/04/2018 adding Pareto, Burr and Normal (E[X] & Var(X)) distribution
16/04/2018 adding Gompertz & TVaR function for binomial and poisson