A continuous distribution in which the logarithm of a variable has a normal
distribution. It is a general case of Gibrat's
distribution, to which the log normal distribution reduces with and . A log normal distribution results if the variable is the
product of a large number of independent, identically-distributed variables in the
same way that a normal distribution results
if the variable is the sum of a large number of independent, identically-distributed
variables.

The probability density and cumulative distribution functions for the log normal distribution are

Examples of variates which have approximately log normal distributions include the size of silver particles in a photographic emulsion, the survival time of bacteria in disinfectants, the weight and blood pressure of humans, and the number of words written in sentences by George Bernard Shaw.