Distributacalcul (version 0.4.0)

Lnorm: Lognormal Distribution

Description

Lognormal distribution with mean \(\mu\) and variance \(\sigma\).

Usage

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)

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.

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.

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 \(x \in \mathcal{R}^{+}\), \(\mu \in \mathcal{R}, \sigma > 0\).

Examples

expValLnorm(meanlog = 3, sdlog = 5)

varLnorm(meanlog = 3, sdlog = 5)

kthMomentLnorm(k = 2, meanlog = 3, sdlog = 5)

expValLimLnorm(d = 2, meanlog = 2, sdlog = 5)

expValTruncLnorm(d = 2, meanlog = 2, sdlog = 5)

# Values greater than d
expValTruncLnorm(d = 2, meanlog = 2, sdlog = 5, less.than.d = FALSE)

stopLossLnorm(d = 2, meanlog = 2, sdlog = 5)

meanExcessLnorm(d = 2, meanlog = 2, sdlog = 5)

VatRLnorm(kap = 0.8, meanlog = 3, sdlog = 5)

TVatRLnorm(kap = 0.8, meanlog = 2, sdlog = 5)