CompBinom: Compound Binomial Distribution

In Distributacalcul: Probability Distribution Functions

Description

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

Usage

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.

Details

The compound binomial distribution has density ....

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.

Examples

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

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

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

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

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")

Distributacalcul documentation built on Sept. 13, 2020, 5:19 p.m.