In probability and statistics, the log-normal distribution is the single-tailed probability distribution of any random variable whose logarithm is normally distributed. If Y is a random variable with a normal distribution, then X = exp(Y) has a log-normal distribution; likewise, if X is log-normally distributed, then log(X) is normally distributed.

A variable might be modeled as log-normal if it can be thought of as the multiplicative product of many small independent factors. For example the long-term return rate on a stock investment can be considered to be the product of the daily return rates.

f(x,mu,sigma) = exp(-0.5 * ( (log(x)-mu)/sigma) ^2 )/(x * sqrt(2 * pi)* sigma)

support 0 ⇐ x ⇐ Inf