Lnorm.Rd
Lognormal 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