# Rev Language Reference

## dnLognormal - Lognormal Distribution

Lognormal distribution is the distribution for a log-transformed normally distributed random variable with mean 'mu' and standard deviation 'sigma'.

• dnLnorm

### Usage

dnLognormal(Real mean, RealPos sd)

### Arguments

 mean : Real (pass by const reference) The mean in log-space (observed mean is exp(m)). sd : RealPos (pass by const reference) The standard deviation in log-space.

### Details

The lognormal random variable is defined as :X = exp(mu + sigma Z) where mu is the mean parameter, sigma is the standard deviation, and Z is a standard normal random variable. Note, in effect, the mean and standard deviation provide the location and scale of the exponentiated normal variate, mu + sigma Z.The lognormal distribution has density: f(x) = 1/(x sigma sqrt(2 pi)) e^-((ln x - mu)^2/(2 sigma^2)) where mu is the mean of the distribution and sigma the standard deviation.

### Example

# set an expected value for x
expectation_of_x <- 1
# set a mean and sd parameter
sd <- 0.5
mean <- ln(expectation_of_x) - 0.5 * sd^2
# create a lognormal distribution with expected value of 1
x ~ dnLognormal(mean=mean, sd=sd)