Lognormal frequency distribution
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
- Frequency distribution
- Leptokurtic frequency distribution
- Lognormally distributed share returns
- Median
- Normal frequency distribution
