Distributacalcul (version 0.2.2)

kthmoment_burr: kth moment of the Burr distribution

Description

kth moment of the Burr distribution with shape parameters \(\alpha\) (shape1) and \(\tau\) (shape2) as well as rate parameter \(\lambda\).

Usage

kthmoment_burr(k, shape1, shape2, rate = 1/scale, scale = 1/rate)

Arguments

k

kth-moment.

shape1

first shape parameter \(\alpha\), must be positive integer.

shape2

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

rate

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

scale

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

Value

Function :

• E_burr gives the expected value.

• V_burr gives the variance.

• kthmoment_burr gives the kth moment.

• Etronq_burr gives the truncated mean.

• SL_burr gives the stop-loss.

• Elim_burr gives the limited mean.

• Mexcess_burr gives the mean excess loss.

• TVaR_burr gives the Tail Value-at-Risk.

• VaR_burr gives the Value-at-Risk.

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

Details

The Burr distribution with rate parameter \(\lambda\) as well as shape parameters \(\alpha\) and \(\tau\) has density: $$f\left(x\right) = \frac{\alpha \tau \lambda^{ \alpha } x^{ \tau - 1 }}{(\lambda + x^{ \tau })^{\alpha +1}}$$ for \(x \in \mathcal{R}^+\), \(\alpha, \tau, \lambda > 0\).

See Also

Other Burr Distribution: E_burr(), Elim_burr(), Etronq_burr(), Mexcess_burr(), SL_burr(), TVaR_burr(), V_burr(), VaR_burr()

Examples

# NOT RUN {
# With scale parameter
kthmoment_burr(k = 1, rate = 2, shape1 = 2, shape2 = 5)

# With rate parameter
kthmoment_burr(k = 1, scale = 0.5, shape1 = 2, shape2 = 5)

# }