Distributacalcul (version 0.2.2)

p_PCOMP: Compound Poisson Distribution

Description

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

Usage

p_PCOMP(
  x,
  lambda,
  shape,
  rate = 1/scale,
  scale = 1/rate,
  k0,
  distr_severity = "Gamma"
)
E_PCOMP(
  lambda,
  shape,
  rate = 1/scale,
  scale = 1/rate,
  distr_severity = "Gamma"
)
V_PCOMP(
  lambda,
  shape,
  rate = 1/scale,
  scale = 1/rate,
  distr_severity = "Gamma"
)
VaR_PCOMP(
  kap,
  lambda,
  shape,
  rate = 1/scale,
  scale = 1/rate,
  k0,
  distr_severity = "Gamma"
)
TVaR_PCOMP(
  kap,
  lambda,
  shape,
  rate = 1/scale,
  scale = 1/rate,
  vark,
  k0,
  distr_severity = "Gamma"
)

Arguments

x

quantile.

lambda

Rate parameter \(\lambda\).

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_PCOMP gives the cumulative density function.

• E_PCOMP gives the expected value.

• V_PCOMP gives the variance.

• TVaR_PCOMP gives the Tail Value-at-Risk.

• VaR_PCOMP gives the Value-at-Risk.

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

Details

The compound Binomial Distribution with parameters ... has density ....

Examples

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

E_PCOMP(lambda = 2, shape = log(1000) - 0.405, rate = 0.9^2,
          distr_severity = "Lognormale")

V_PCOMP(lambda = 2, shape = log(1000) - 0.405, rate = 0.9^2,
          distr_severity = "Lognormale")

VaR_PCOMP(kap = 0.9, lambda = 2, shape = log(1000) - 0.405,
            rate = 0.9^2, k0 = 1E2, distr_severity = "Gamma")

vark_calc <- VaR_PCOMP(kap = 0.9, lambda = 2, shape = 0.59,
            rate = 0.9^2, k0 = 1E2, distr_severity = "Gamma")
TVaR_PCOMP(kap = 0.9, lambda = 2, shape = 0.59, rate = 0.9^2,
            vark = vark_calc, k0 = 1E2, distr_severity = "Gamma")

# }