Moment Generating Function (MGF) of the Erlang distribution with shape parameter \(n\) and rate parameter \(\beta\).
MGF_erlang(t, shape, rate = 1/scale, scale = 1/rate)t.
shape parameter \(n\), must be positive integer.
\(\beta\) is the rate parameter, must be positive.
alternative parameterization to rate parameter, scale = 1 / rate.
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.
Etronq_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.
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 \(x \in \mathcal{R}^+\), \(\beta > 0\), \(n \in \mathcal{N}^+\)
Other Erlang Distribution:
E_erlang(),
Elim_erlang(),
Etronq_erlang(),
Mexcess_erlang(),
SL_erlang(),
TVaR_erlang(),
V_erlang(),
VaR_erlang(),
derlang(),
kthmoment_erlang(),
perlang()
# NOT RUN {
MGF_erlang(t = 1, shape = 3, rate = 5)
# }
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