CompNBinom.Rd
Computes various risk measures (mean, variance, Value-at-Risk (VatR), and Tail Value-at-Risk (TVatR)) for the compound Negative Binomial distribution.
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" )
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.
|
kap | probability. |
vark | Value-at-Risk (VaR) calculated at the given probability kap. |
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.
The compound negative binomial distribution has density ....
pCompNBinom(x = 2, size = 1, prob = 0.2, shape = log(1000) - 0.405, rate = 0.9^2, k0 = 1E2, distr_severity = "Gamma")#> [1] 0.2004906expValCompNBinom(size = 4, prob = 0.2, shape = 0, scale = 1, distr_severity = "Lognormal")#> [1] 26.37954varCompNBinom(size = 1, prob = 0.2, shape = log(1000) - 0.405, rate = 0.9^2, distr_severity = "Lognormale")#> [1] 5011632VatRCompNBinom(kap = 0.9, size = 1, prob = 0.2, shape = 0.59, rate = 0.9^2, k0 = 1E2, distr_severity = "Gamma")#> [1] 7.833102vark_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")#> [1] 11.75336