Distributacalcul (version 0.2.2)

SL_burr: Stop-loss of the Burr distribution

Description

Stop-loss of the Burr distribution with shape parameters $\alpha$ (shape1) and $\tau$ (shape2) as well as rate parameter $\lambda$.

Usage

SL_burr(d, shape1, shape2, rate = 1/scale, scale = 1/rate)

Arguments

d

cut-off value.

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(), TVaR_burr(), V_burr(), VaR_burr(), kthmoment_burr()

Examples

# NOT RUN {
# With scale parameter
SL_burr(d = 2, rate = 2, shape1 = 2, shape2 = 5)

# With rate parameter
SL_burr(d = 2, scale = 0.5, shape1 = 2, shape2 = 5)

# }