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)location parameter \(\mu\).
standard deviation \(\sigma\), must be positive.
kth-moment.
cut-off value.
logical; if TRUE (default) truncated mean for values <= d, otherwise, for values > d.
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] 5389698
varLnorm(meanlog = 3, sdlog = 5)
#> [1] 2.091659e+24
kthMomentLnorm(k = 2, meanlog = 3, sdlog = 5)
#> [1] 2.091659e+24
expValLimLnorm(d = 2, meanlog = 2, sdlog = 5)
#> [1] 1.347946
expValTruncLnorm(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] 1982759
stopLossLnorm(d = 2, meanlog = 2, sdlog = 5)
#> [1] 1982758
meanExcessLnorm(d = 2, meanlog = 2, sdlog = 5)
#> [1] 3287629
VatRLnorm(kap = 0.8, meanlog = 3, sdlog = 5)
#> [1] 1350.333
TVatRLnorm(kap = 0.8, meanlog = 2, sdlog = 5)
#> [1] 9913637