# CompNBinom: Compound Negative Binomial Distribution In Distributacalcul: Probability Distribution Functions

## Description

Computes various risk measures (mean, variance, Value-at-Risk (VatR), and Tail Value-at-Risk (TVatR)) for the compound Negative Binomial 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 47 48 49 50 51``` ```pCompNBinom( x, size, prob, shape, rate = 1/scale, scale = 1/rate, k0, distr_severity = "Gamma" ) expValCompNBinom( size, prob, shape, rate = 1/scale, scale = 1/rate, distr_severity = "Gamma" ) varCompNBinom( size, prob, shape, rate = 1/scale, scale = 1/rate, distr_severity = "Gamma" ) VatRCompNBinom( kap, size, prob, shape, rate = 1/scale, scale = 1/rate, k0, distr_severity = "Gamma" ) TVatRCompNBinom( kap, vark, size, prob, shape, rate = 1/scale, scale = 1/rate, k0, distr_severity = "Gamma" ) ```

## Arguments

 `x` vector of quantiles. `size` Number of successful trials. `prob` Probability of success in each trial. `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 negative binomial distribution has density ....

## Value

Function :

• `pCompNBinom` gives the cumulative density function.

• `expValCompNBinom` gives the expected value.

• `varCompNBinom` gives the variance.

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

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

Returned values are approximations for the cumulative density function, TVatR, and VatR.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```pCompNBinom(x = 2, size = 1, prob = 0.2, shape = log(1000) - 0.405, rate = 0.9^2, k0 = 1E2, distr_severity = "Gamma") expValCompNBinom(size = 4, prob = 0.2, shape = 0, scale = 1, distr_severity = "Lognormal") varCompNBinom(size = 1, prob = 0.2, shape = log(1000) - 0.405, rate = 0.9^2, distr_severity = "Lognormale") VatRCompNBinom(kap = 0.9, size = 1, prob = 0.2, shape = 0.59, rate = 0.9^2, k0 = 1E2, distr_severity = "Gamma") vark_calc <- VatRCompNBinom(kap = 0.9, size = 1, prob = 0.2, shape = 0.59, rate = 0.9^2, k0 = 1E2, distr_severity = "Gamma") TVatRCompNBinom(kap = 0.9, size = 1, prob = 0.2, 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.