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

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.

## 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.

## Details

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

## Examples

pCompPois(x = 2, lambda = 2, shape = log(1000) - 0.405,
rate = 0.9^2, k0 = 1E2, distr_severity = "Gamma")
#> [1] 0.1361652

expValCompPois(lambda = 2, shape = log(1000) - 0.405, rate = 0.9^2,
distr_severity = "Lognormale")
#> [1] 2000

varCompPois(lambda = 2, shape = log(1000) - 0.405, rate = 0.9^2,
distr_severity = "Lognormale")
#> [1] 4495816

VatRCompPois(kap = 0.9, lambda = 2, shape = log(1000) - 0.405,
rate = 0.9^2, k0 = 1E2, distr_severity = "Gamma")
#> [1] 32.63546

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")
#> [1] 5.352432