# Log-normal distribution

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In probability theory, a log-normal distribution is a probability distribution of a 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 Y = log(X) is normally distributed. (This is true regardless of the base of the logarithmic function: if loga(Y) is normally distributed, then so is logb(Y), for any two positive numbers ab ≠ 1.)

Log-normal is also written log normal or lognormal. It is occasionally referred to as the Galton distribution or Galton's distribution, after Francis Galton.

A variable might be modeled as log-normal if it can be thought of as the multiplicative product of many independent random variables each of which is positive. For example, in finance, a long-term discount factor can be derived from the product of short-term discount factors. In wireless communication, the attenuation caused by shadowing or slow fading from random objects is often assumed to be log-normally distributed. See log-distance path loss model.