CompNBinom.Rd
Computes various risk measures (mean, variance, ValueatRisk (VatR), and Tail ValueatRisk (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  ValueatRisk (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 ValueatRisk.
VatRCompNBinom
gives the ValueatRisk.
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