# CompPois: Compound Poisson Distribution In Distributacalcul: Probability Distribution Functions

## Description

Computes various risk measures (mean, variance, Value-at-Risk (VaR), and Tail Value-at-Risk (TVaR)) for the compound Poisson distribution.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46``` ```pCompPois( x, lambda, shape, rate = 1/scale, scale = 1/rate, k0, distr_severity = "Gamma" ) expValCompPois( lambda, shape, rate = 1/scale, scale = 1/rate, distr_severity = "Gamma" ) varCompPois( lambda, shape, rate = 1/scale, scale = 1/rate, distr_severity = "Gamma" ) VatRCompPois( kap, lambda, shape, rate = 1/scale, scale = 1/rate, k0, distr_severity = "Gamma" ) TVatRCompPois( kap, lambda, shape, rate = 1/scale, scale = 1/rate, vark, k0, distr_severity = "Gamma" ) ```

## Arguments

 `x` vector of quantiles. `lambda` Rate parameter lambda. `shape` shape parameter alpha, must be positive. `rate` rate parameter beta, must be positive. `scale` alternative parameterization to the rate parameter, scale = 1 / rate. `k0` point up to which to sum the distribution for the approximation. `distr_severity` Choice of severity distribution. "gamma" (default) "lognormal" only for the expected value and variance. `kap` probability. `vark` Value-at-Risk (VaR) calculated at the given probability kap.

## Details

The compound Poisson distribution with parameters ... has density ....

## Value

Function :

• `pCompPois` gives the cumulative density function.

• `expValCompPois` gives the expected value.

• `varCompPois` gives the variance.

• `TVatRCompPois` gives the Tail Value-at-Risk.

• `VatRCompPois` gives the Value-at-Risk.

Returned values are approximations for the cumulative density function, TVaR, and VaR.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```pCompPois(x = 2, lambda = 2, shape = log(1000) - 0.405, rate = 0.9^2, k0 = 1E2, distr_severity = "Gamma") expValCompPois(lambda = 2, shape = log(1000) - 0.405, rate = 0.9^2, distr_severity = "Lognormale") varCompPois(lambda = 2, shape = log(1000) - 0.405, rate = 0.9^2, distr_severity = "Lognormale") VatRCompPois(kap = 0.9, lambda = 2, shape = log(1000) - 0.405, rate = 0.9^2, k0 = 1E2, distr_severity = "Gamma") vark_calc <- VatRCompPois(kap = 0.9, lambda = 2, shape = 0.59, rate = 0.9^2, k0 = 1E2, distr_severity = "Gamma") TVatRCompPois(kap = 0.9, lambda = 2, shape = 0.59, rate = 0.9^2, vark = vark_calc, k0 = 1E2, distr_severity = "Gamma") ```

Distributacalcul documentation built on Sept. 13, 2020, 5:19 p.m.