# Lnorm: Lognormal Distribution In Distributacalcul: Probability Distribution Functions

## Description

Lognormal distribution with mean mu and variance sigma.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```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.