Value-at-Risk of the Erlang distribution

Value-at-Risk of the Erlang distribution with shape parameter \(n\) and rate parameter \(\beta\).

VaR_erlang(kap, shape, rate = 1/scale, scale = 1/rate)

Arguments

kap	probability.
shape	shape parameter \(n\), must be positive integer.
rate	\(\beta\) is the rate parameter, must be positive.
scale	alternative parameterization to rate parameter, scale = 1 / rate.

Value

Function :

• MGF_erlang gives the moment generating function (MGF).

• derlang gives the density function.

• perlang gives the cumulative density function.

• E_erlang gives the expected value.

• V_erlang gives the variance.

• kthmoment_erlang gives the kth moment.

• Etrunc_erlang gives the truncated mean.

• SL_erlang gives the stop-loss.

• Elim_erlang gives the limited mean.

• Mexcess_erlang gives the mean excess loss.

• TVaR_erlang gives the Tail Value-at-Risk.

• VaR_erlang gives the Value-at-Risk.

Invalid parameter values will return an error detailing which parameter is problematic.

Details

The Erlang distribution with shape parameter \(n\) and rate parameter \(\beta\) has density: $$f\left(x\right) = \frac{\beta^{n}}{\Gamma(n)} x^{n - 1}% \mathrm{e}^{-\beta x}$$ for \(x \in \mathcal{R}^+\), \(\beta > 0\), \(n \in \mathcal{N}^+\)

Note

Wrapper of qgamma from package stats.

See also

Other Erlang Distribution: E_erlang(), Elim_erlang(), Etrunc_erlang(), MGF_erlang(), Mexcess_erlang(), SL_erlang(), TVaR_erlang(), V_erlang(), derlang(), kthmoment_erlang(), perlang()

Examples

# With scale parameter
VaR_erlang(kap = .2, shape = 3, scale = 4)
#> [1] 6.140177

# With rate parameter
VaR_erlang(kap = .2, shape = 3, rate = 0.25)
#> [1] 6.140177