Distributacalcul

The goal of Distributacalcul is to simplify the life of students and scientists by offering premade functions for various functions of probability distributions. Functions calculate moments of the distribution (mean, variance, kth moment) as well as the expected value of functions of the distribution (truncated mean, stop-loss, mean excess loss, etc.). In addition, the package includes some risk measures (Value-at-Risk and Tail Value-at-Risk).

This package depends primarily the stats package.

Installation

You can install the released version of Distributacalcul from CRAN with:

install.packages("Distributacalcul")

And the development version from GitHub with:

# install.packages("devtools")
devtools::install_github("alec42/Distributacalcul_Package")

Example

This is a basic example which shows you the typical use of the functions:

library(Distributacalcul)
##  Various moments:
E_beta(shape1 = 2, shape2 = 4) # E[X]
#> [1] 0.3333333
V_beta(shape1 = 2, shape2 = 4) # V(X)
#> [1] 0.03174603
kthmoment_beta(k = 3, shape1 = 2, shape2 = 4) # E[X^k]
#> [1] 0.07142857

##  Expected value of functions:
Elim_beta(d = 0.3, shape1 = 2, shape2 = 4) # E[min(X; d)]
#> [1] 2.19811
Etronq_beta(d = .3, shape1 = 2, shape2 = 4, less.than.d = TRUE) # E[X * 1_{X <= d}]
#> [1] 0.08523
Etronq_beta(d = .3, shape1 = 2, shape2 = 4, less.than.d = FALSE) # E[X * 1_{X > d}]
#> [1] 0.2481033
Mexcess_beta(d = .3, shape1 = 2, shape2 = 4) # E[(X - d | X > d)]
#> [1] 0.169697
SL_beta(d = .3, shape1 = 2, shape2 = 4) # E[max(X - d, 0)]
#> [1] 0.4065693

##  Risk measures:
TVaR_beta(kap = 0.99, shape1 = 2, shape2 = 4) # TVaR_{k}(X)
#> [1] 0.8239414
VaR_beta(kap = 0.99, shape1 = 2, shape2 = 4) # VaR_{k}(X) = F_X^(-1)(k)
#> [1] 0.7779277

Syntax:

Function	Syntax
Mean	E_distribution
K-th moment	kthmoment_distribution
Truncated mean	Etronq_distribution
Limited expected value	Elim_distribution
Variance	V_distribution
Stop-loss	SL_distribution
Excess of mean	Mexcess_distribution
Moment Generating Function	MGF_distribution
Probability Generating Function	PGF_distribution
Density	ddistribution
Cumulative density function	pdistribution
Value-at-Risk (percentile)	TVaR_distribution
Tail Value-at-Risk	VaR_distribution

Included distributions and functions

Continuous distributions

	Erlang	Inverse Gaussian	Weibull	Burr
Mean	X	X	X	X
kth moment	X		X	X
Variance	X	X	X	X
Truncated mean	X	X	X	X
Limited mean	X	X	X	X
Stop-loss	X	X	X	X
Excess of mean	X	X	X	X
Moment Generating Function	X	X
Probability Density Function	X
Cumulative Probability Density Function	X
Value-at-Risk	X	X	X	X
Tail Value-at-Risk	X	X	X	X

Table continues below

	Log-logistic	Beta	Gamma	Pareto
Mean	X	X	X	X
kth moment	X	X	X	X
Variance	X	X	X	X
Truncated mean	X	X	X	X
Limited mean	X	X	X	X
Stop-loss	X	X	X	X
Excess of mean	X	X	X	X
Moment Generating Function		X	X
Probability Density Function
Cumulative Probability Density Function
Value-at-Risk	X	X	X	X
Tail Value-at-Risk	X	X	X	X

Table continues below

	Lognormal	Exponential	Uniform	Normal
Mean	X	X	X	X
kth moment	X	X	X
Variance	X	X	X	X
Truncated mean	X	X	X	X
Limited mean	X	X	X	X
Stop-loss	X	X	X	X
Excess of mean	X	X	X	X
Moment Generating Function		X		X
Probability Density Function
Cumulative Probability Density Function
Value-at-Risk	X	X	X	X
Tail Value-at-Risk	X	X	X	X

Discrete distributions

	Binomial	Negative Binomial	Poisson
Mean	X	X	X
kth moment
Variance	X	X	X
Truncated mean	X	X	X
Limited mean
Stop-loss
Excess of mean
Moment Generating Function	X	X	X
Probability Generating Function	X	X	X
Probability Density Function
Cumulative Probability Density Function
Value-at-Risk	X
Tail Value-at-Risk	X	X	X

Table continues below

	Uniform	Logarithmic	Hypergeometric
Mean	X	X	X
kth moment
Variance	X	X	X
Truncated mean
Limited mean
Stop-loss
Excess of mean
Moment Generating Function		X
Probability Generating Function		X
Probability Density Function	X
Cumulative Probability Density Function	X
Value-at-Risk
Tail Value-at-Risk

Updates

Date	Modifications
26/07/2019	Initial creation of package
12/09/2019	Completion of creation of all necessary function files
17/11/2019	Merger of tvarPackage, beginning of documentation creation.
20/05/2020	Addition of Shiny component.
02/06/2020	Completion of documentation, first attempt of a submission to CRAN.
02/07/2020	Modifications according to CRAN’s notes, version 0.2.0.