Lnorm.RdLognormal distribution with mean \(\mu\) and variance \(\sigma\).
expValLnorm(meanlog, sdlog) varLnorm(meanlog, sdlog) kthMomentLnorm(k, meanlog, sdlog) expValLimLnorm(d, meanlog, sdlog) expValTruncLnorm(d, meanlog, sdlog, less.than.d = TRUE) stopLossLnorm(d, meanlog, sdlog) meanExcessLnorm(d, meanlog, sdlog) VatRLnorm(kap, meanlog, sdlog) TVatRLnorm(kap, meanlog, sdlog)
| meanlog | location parameter \(\mu\). |
|---|---|
| sdlog | standard deviation \(\sigma\), must be positive. |
| k | kth-moment. |
| d | cut-off value. |
| less.than.d | logical; if |
| kap | probability. |
Function :
expValLnorm gives the expected value.
varLnorm gives the variance.
kthMomentLnorm gives the kth moment.
expValLimLnorm gives the limited mean.
expValTruncLnorm gives the truncated mean.
stopLossLnorm gives the stop-loss.
meanExcessLnorm gives the mean excess loss.
VatRLnorm gives the Value-at-Risk.
TVatRLnorm gives the Tail Value-at-Risk.
Invalid parameter values will return an error detailing which parameter is problematic.
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 \(x \in \mathcal{R}^{+}\), \(\mu \in \mathcal{R}, \sigma > 0\).
Function VatRLnorm is a wrapper of the qlnorm
function from the stats package.
expValLnorm(meanlog = 3, sdlog = 5)#> [1] 5389698varLnorm(meanlog = 3, sdlog = 5)#> [1] 2.091659e+24kthMomentLnorm(k = 2, meanlog = 3, sdlog = 5)#> [1] 2.091659e+24expValLimLnorm(d = 2, meanlog = 2, sdlog = 5)#> [1] 1.347946expValTruncLnorm(d = 2, meanlog = 2, sdlog = 5)#> [1] 0.1417529# Values greater than d expValTruncLnorm(d = 2, meanlog = 2, sdlog = 5, less.than.d = FALSE)#> [1] 1982759stopLossLnorm(d = 2, meanlog = 2, sdlog = 5)#> [1] 1982758meanExcessLnorm(d = 2, meanlog = 2, sdlog = 5)#> [1] 3287629VatRLnorm(kap = 0.8, meanlog = 3, sdlog = 5)#> [1] 1350.333TVatRLnorm(kap = 0.8, meanlog = 2, sdlog = 5)#> [1] 9913637