CompBinom.Rd
Computes various risk measures (mean, variance, Value-at-Risk (VaR), and Tail Value-at-Risk (TVaR)) for the compound Binomial distribution.
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" )
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.
|
kap | probability. |
vark | Value-at-Risk (VaR) calculated at the given probability kap. |
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.
The compound binomial distribution has density ....
pCompBinom(x = 2, size = 1, prob = 0.2, shape = log(1000) - 0.405, rate = 0.9^2, k0 = 1E2, distr_severity = "Gamma")#> [1] 0.8006133expValCompBinom(size = 1, prob = 0.2, shape = log(1000) - 0.405, rate = 0.9^2, distr_severity = "Lognormale")#> [1] 200varCompBinom(size = 1, prob = 0.2, shape = log(1000) - 0.405, rate = 0.9^2, distr_severity = "Lognormale")#> [1] 409581.6VatRCompBinom(kap = 0.9, size = 1, prob = 0.2, shape = log(1000) - 0.405, rate = 0.9^2, k0 = 1E2, distr_severity = "Gamma")#> [1] 7.620525vark_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")#> [1] 1.326515