## DEFINITION of 'Log-Normal Distribution'

A statistical distribution of random variables which have a normally distributed logarithm. Log-normal distributions can model a random variable *X* where log(*X*) is normally distributed.

These distributions, under multiplication and division, are self-replicating. That is to say, multiplying or dividing log-normal random variables will result in log-normal distributions.

## BREAKING DOWN 'Log-Normal Distribution'

For example, log-normal distributions can model certain instances, such as the change in price distribution of a stock, or commodity positions. This is because the time series creates random variables. By taking the natural log of each of the random variables, the resulting set of numbers will be log-normally distributed. Other uses include survival rates of cancer patients or failure rates in product tests.