Lognormal frequency distribution: Difference between revisions
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A simplified illustration is set out below. | A simplified illustration is set out below. | ||
A simple (non-symmetrical) lognormal distribution includes the following values: | A simple (non-symmetrical) lognormal distribution includes the following values: | ||
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The median - the mid-point of the distribution - being 1. | 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. | 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. | ||
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= -2, -1, 0, 1 and 2. | = -2, -1, 0, 1 and 2. | ||
When the parent values are lognormally distributed, the transformed (log) values follow a (symmetrical) normal distribution. | When the parent values are lognormally distributed, the transformed (log) values follow a (symmetrical) normal distribution. | ||
Revision as of 10:18, 22 June 2014
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.
