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)

## Arguments

meanlog

location parameter $$\mu$$.

sdlog

standard deviation $$\sigma$$, must be positive.

k

kth-moment.

d

cut-off value.

less.than.d

logical; if TRUE (default) truncated mean for values <= d, otherwise, for values > d.

kap

probability.

## Value

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.

## 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 $$x \in \mathcal{R}^{+}$$, $$\mu \in \mathcal{R}, \sigma > 0$$.

## Note

Function VatRLnorm is a wrapper of the qlnorm function from the stats package.

## Examples

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