Lognormal frequency distribution

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A lognormal distribution is one where the logarithm - for example log(X) or ln(X) - of the variable is normally distributed.

Lognormal distributions have a minimum - usually 'worst case' - value, whilst having an infinitely high upside.

A simplified illustration is set out below.

A simple (non-symmetrical) lognormal distribution includes the following values:

0.01, 0.1, 1, 10 and 100.

The median - the mid-point of the distribution - being 1.

This distribution is skewed: most of the values being in the lower (left) part of the distribution, the upside being infinitely high, and the downside limit being 0.

The logs - for example to the base 10 - of these values are:

log(0.01), log(0.1), log(1), log(10) and log(100)

= -2, -1, 0, 1 and 2.

When the parent values are lognormally distributed, the transformed (log) values follow a (symmetrical) normal distribution.

So for example the mean, mode and median of the log values above (including -2, -1, 0, 1 and 2) would all be the same, namely the middle value 0.

See also