# CompBinom: Compound Binomial 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 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``` ```pCompBinom( x, size, prob, shape, rate = 1/scale, scale = 1/rate, k0, distr_severity = "Gamma" ) expValCompBinom( size, prob, shape, rate = 1/scale, scale = 1/rate, distr_severity = "Gamma" ) varCompBinom( size, prob, shape, rate = 1/scale, scale = 1/rate, distr_severity = "Gamma" ) VatRCompBinom( kap, size, prob, shape, rate = 1/scale, scale = 1/rate, k0, distr_severity = "Gamma" ) TVatRCompBinom( kap, size, prob, shape, rate = 1/scale, scale = 1/rate, vark, k0, distr_severity = "Gamma" ) ```

## Arguments

 `x` vector of quantiles. `size` Number of trials (0 or more). `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 binomial distribution has density ....

## Value

Function :

• `pCompBinom` gives the cumulative density function.

• `expValCompBinom` gives the expected value.

• `varCompBinom` gives the variance.

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

• `VatRCompBinom` 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``` ```pCompBinom(x = 2, size = 1, prob = 0.2, shape = log(1000) - 0.405, rate = 0.9^2, k0 = 1E2, distr_severity = "Gamma") expValCompBinom(size = 1, prob = 0.2, shape = log(1000) - 0.405, rate = 0.9^2, distr_severity = "Lognormale") varCompBinom(size = 1, prob = 0.2, shape = log(1000) - 0.405, rate = 0.9^2, distr_severity = "Lognormale") VatRCompBinom(kap = 0.9, size = 1, prob = 0.2, shape = log(1000) - 0.405, rate = 0.9^2, k0 = 1E2, distr_severity = "Gamma") vark_calc <- VatRCompBinom(kap = 0.9, size = 1, prob = 0.2, shape = 0.59, rate = 0.9^2, k0 = 1E2, distr_severity = "Gamma") TVatRCompBinom(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.