The Log-normal distribution reference article from the English Wikipedia on 24-Apr-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Log-normal distribution

In probability and statistics, the log-normal distribution is a probability distribution which is closely related to the normal distribution: if X is a random variable with a normal distribution, then exp(X) has a log-normal distribution. In other words: the natural logarithm of a log-normally distributed variable is normally distributed.

"Log-normal" is also written "log normal" or "lognormal".

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

The log-normal distribution has probability density function

for x > 0, where μ and σ are the mean and standard deviation of the variable's logarithm. The expected value is

and the variance is

.

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