Compound Binomial Distribution

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"
)

Arguments

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. "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 :

• 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.

Details

The compound binomial distribution has density ....

Examples

pCompBinom(x = 2, size = 1, prob = 0.2, shape = log(1000) - 0.405,
          rate = 0.9^2, k0 = 1E2, distr_severity = "Gamma")
#> [1] 0.8006133

expValCompBinom(size = 1, prob = 0.2, shape = log(1000) - 0.405, rate = 0.9^2,
          distr_severity = "Lognormale")
#> [1] 200

varCompBinom(size = 1, prob = 0.2, shape = log(1000) - 0.405, rate = 0.9^2,
          distr_severity = "Lognormale")
#> [1] 409581.6

VatRCompBinom(kap = 0.9, size = 1, prob = 0.2, shape = log(1000) - 0.405,
            rate = 0.9^2, k0 = 1E2, distr_severity = "Gamma")
#> [1] 7.620525

vark_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