CompNBinom {Distributacalcul}

Compound Negative Binomial Distribution

Description

Computes various risk measures (mean, variance, Value-at-Risk (VatR), and Tail Value-at-Risk (TVatR)) for the compound Negative Binomial distribution.

Usage

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"
)

Arguments

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.

• "gamma" (default)

• "lognormal" only for the expected value and variance.

kap

probability.

vark

Value-at-Risk (VaR) calculated at the given probability kap.

Details

The compound negative binomial distribution has density ....

Value

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.

Examples

pCompNBinom(x = 2, size = 1, prob = 0.2, shape = log(1000) - 0.405,
          rate = 0.9^2, k0 = 1E2, distr_severity = "Gamma")


expValCompNBinom(size = 4, prob = 0.2, shape = 0, scale = 1,
         distr_severity = "Lognormal")

varCompNBinom(size = 1, prob = 0.2, shape = log(1000) - 0.405, rate = 0.9^2,
          distr_severity = "Lognormale")

VatRCompNBinom(kap = 0.9, size = 1, prob = 0.2, shape = 0.59,
            rate = 0.9^2, k0 = 1E2, distr_severity = "Gamma")

vark_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")