README.md

In gabrielcrepeault/tvarPackage: Calculate Mean, Variance, Truncated Mean, VaR, TVaR, etc for different probability distributions

permalink: docs/index.html

tvarPackage

This package is no longer maintained. Please refer to the Distributacalcul_Package.

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| |11/12/2018 | create website to vizualise tvarPackage help|

gabrielcrepeault/tvarPackage documentation built on April 21, 2020, 3:25 p.m.