CompPois.Rd
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" )
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.
|
kap | probability. |
vark | Value-at-Risk (VaR) calculated at the given probability kap. |
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.
The compound Poisson distribution with parameters ... has density ....
pCompPois(x = 2, lambda = 2, shape = log(1000) - 0.405, rate = 0.9^2, k0 = 1E2, distr_severity = "Gamma")#> [1] 0.1361652#> [1] 2000#> [1] 4495816VatRCompPois(kap = 0.9, lambda = 2, shape = log(1000) - 0.405, rate = 0.9^2, k0 = 1E2, distr_severity = "Gamma")#> [1] 32.63546vark_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