rlnorm

Description

rlnorm returns a sample from the log-normal distribution. A log-normal distribution is one in which LN(X) is normally distributed. It occurs when there are a number of independent sources of variability whose errors are multiplicative. Log-normal distributions are used to describe a number of natural phenomena such as pollutant concentrations where the values are usually small and non-negative but with long tails.

Syntax

rlnorm([rows=1], [cols=1], [mean=0], [stdev=1], [seed_str]) where

rows and cols describe the shape of the output
mean ( $\mu$ ) and stdev ( $\sigma$ ) are the parameters of the distribution. By default the function returns the standard lognormal distribution, where LN(X) follows a standard normal distribution.
seed_str is a memorable seed string. If omitted then a quasi-unique seed is used to generate a non-volatile output; see the documentation of runif for more detail about this. Use a memorable string of your choosing if you want to set an explicit seed for reproducibility purposes, and use GetSeed if you want a volatile output.

Note that the distribution parameters $\mu$ and $\sigma$ do NOT describe the mean and standard deviation on the linear scale. Those are given below:

\begin{align*} \mu_X\ &= \exp \left( \mu + \frac{\sigma^2}{2} \right) \\ \sigma^2_X\ &= [\exp(\sigma^2) - 1] \exp(2\mu + \sigma^2) \end{align*}

where $\mu_X$ and $\sigma_X$ describe the mean and standard deviation on the linear scale.

Leaving the seed_str blank is fine for quick & dirty work but for simulation demos you will either want to set the seed with a memorable string or make the function volatile with GetSeed. Please read the caveats about choosing seed strings in the runif documentation; they apply to this function too.

Example

The example below compares the distribution of 100 draws from the standard log-normal distribution to the theoretical probability density function.

100 draws from rlnorm with mu 0 and sigma 1, shown as a jitterplot under the right-skewed lognormal density

Download: rlnorm.xlsx

Source Code

rlnorm = LAMBDA(
    [rows], [cols],     // size of output
    [mean], [stdev],    // mean and std dev of log-transformed variable
    [seed_str],       // optional seed string (default uses this workbook's CLS_SystemSeed)
    LET(
        rows, IF(ISOMITTED(rows), 1, rows),
        cols, IF(ISOMITTED(cols), 1, cols),
        mean, IF(ISOMITTED(mean), 0, mean),
        stdev, IF(ISOMITTED(stdev), 1, stdev),
        seed_str, IF(
            ISOMITTED(seed_str),
            CLS_SystemSeed & ADDRESS(ROW(),COLUMN()) & "rlnorm",
            seed_str
            ),
        LOGNORM.INV(runif(rows, cols,,,,seed_str), mean, stdev)
    )
);

rnorm rerror