Lnorm: Lognormal Distribution

In Distributacalcul: Probability Distribution Functions

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)

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:

f(x) = e^(-(1/2) ((ln(x) - mu)/sigma)^2) / ((2 pi)^(1/2) sigma x

for x >= 0, mu real, sigma > 0.

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.

Note

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

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)

Distributacalcul documentation built on Sept. 13, 2020, 5:19 p.m.