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:

Included distributions and functions

Continuous distributions

Table continues below

Table continues below

Discrete distributions

Table continues below

Updates