Distributacalcul (version 0.2.2)

p_BNCOMP: Compound Negative Binomial Distribution

Description

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

Usage

p_BNCOMP(
  x,
  size,
  prob,
  shape,
  rate = 1/scale,
  scale = 1/rate,
  k0,
  distr_severity = "Gamma"
)
E_BNCOMP(
  size,
  prob,
  shape,
  rate = 1/scale,
  scale = 1/rate,
  distr_severity = "Gamma"
)
V_BNCOMP(
  size,
  prob,
  shape,
  rate = 1/scale,
  scale = 1/rate,
  distr_severity = "Gamma"
)
VaR_BNCOMP(
  kap,
  size,
  prob,
  shape,
  rate = 1/scale,
  scale = 1/rate,
  k0,
  distr_severity = "Gamma"
)
TVaR_BNCOMP(
  kap,
  vark,
  size,
  prob,
  shape,
  rate = 1/scale,
  scale = 1/rate,
  k0,
  distr_severity = "Gamma"
)

Arguments

x

quantile.

size

Number of successful trials.

prob

Probability of success in each trial.

shape

shape parameter \(\alpha\), must be positive integer.

rate

\(\beta\) is the rate parameter, must be positive.

scale

alternative parameterization to 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 :

• p_BNCOMP gives the cumulative density function.

• E_BNCOMP gives the expected value.

• V_BNCOMP gives the variance.

• TVaR_BNCOMP gives the Tail Value-at-Risk.

• VaR_BNCOMP gives the Value-at-Risk.

Returned values are approximations for the cumulative density function, TVaR, and VaR.

Details

The compound Negative Binomial Distribution has density ....

Examples

# NOT RUN {
p_BNCOMP(x = 2, size = 1, prob = 0.2, shape = log(1000) - 0.405,
          rate = 0.9^2, k0 = 1E2, distr_severity = "Gamma")


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

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

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

vark_calc <- VaR_BNCOMP(kap = 0.9, size = 1, prob = 0.2, shape = 0.59,
            rate = 0.9^2, k0 = 1E2, distr_severity = "Gamma")
TVaR_BNCOMP(kap = 0.9, size = 1, prob = 0.2, shape = 0.59, rate = 0.9^2,
            vark = vark_calc, k0 = 1E2, distr_severity = "Gamma")

# }