Distributacalcul (version 0.2.2)

kthmoment_weibull: kth moment of the Weibull distribution

Description

kth moment of the Weibull distribution with shape parameter parameter \(\tau\) and rate parameter \(\beta\).

Usage

kthmoment_weibull(k, shape, rate = 1/scale, scale = 1/rate)

Arguments

k

kth-moment.

shape

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

rate

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

scale

alternative parameterization to rate parameter, scale = 1 / rate.

Value

Returns numeric value. Function :

• E_weibull gives the expected value.

• V_weibull gives the variance.

• kthmoment_weibull gives the kth moment.

• Etronq_weibull gives the truncated mean.

• SL_weibull gives the stop-loss.

• Elim_weibull gives the limited mean.

• Mexcess_weibull gives the mean excess loss.

• TVaR_weibull gives the Tail Value-at-Risk.

• VaR_weibull gives the Value-at-Risk.

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

Details

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

See Also

Other Weibull Distribution: E_weibull(), Elim_weibull(), Etronq_weibull(), Mexcess_weibull(), SL_weibull(), TVaR_weibull(), V_weibull(), VaR_weibull()

Examples

# NOT RUN {
# With scale parameter
kthmoment_weibull(k = 2, shape = 2, scale = 5)

# With rate parameter
kthmoment_weibull(k = 2, shape = 2, rate = 0.2)

# }