Distributacalcul (version 0.2.2)

SL_lnorm: Stop-loss of the Lognormal distribution

Description

Stop-loss of the Lognormal distribution with mean \(\mu\) and variance \(\sigma\).

Usage

SL_lnorm(d, meanlog, sdlog)

Arguments

d

cut-off value.

meanlog

location parameter \(\mu\).

sdlog

standard deviation \(\sigma\), must be positive.

Value

Function :

• E_lnorm gives the expected value.

• V_lnorm gives the variance.

• kthmoment_lnorm gives the kth moment.

• Etronq_lnorm gives the truncated mean.

• SL_lnorm gives the stop-loss.

• Elim_lnorm gives the limited mean.

• Mexcess_lnorm gives the mean excess loss.

• TVaR_lnorm gives the Tail Value-at-Risk.

• VaR_lnorm gives the Value-at-Risk.

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

Details

The Log-normal distribution with mean \(\mu\) and standard deviation \(\sigma\) has density: $$\frac{1}{\sqrt{2\pi}\sigma x}\textrm{e}^{-\frac{1}{2}\left(\frac{\ln(x) - \mu}{\sigma}\right)^2}$$ for \(x \in \mathcal{R}^{+}\), \(\mu \in \mathcal{R}, \sigma > 0\).

See Also

Other Lognormal distribution: E_lnorm(), Elim_lnorm(), Etronq_lnorm(), Mexcess_lnorm(), TVaR_lnorm(), V_lnorm(), VaR_lnorm(), kthmoment_lnorm()

Examples

# NOT RUN {
SL_lnorm(d = 2, meanlog = 2, sdlog = 5)

# }