Lognormal frequency distribution: Difference between revisions

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


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A simple (non-symmetrical) lognormal distribution includes the following values:
A simple (non-symmetrical) lognormal distribution includes the following values:
0.01, 0.1, 1, 10 and 100.
0.01, 0.1, 1, 10 and 100.


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log(0.01), log(0.1), log(1), log(10) and log(100)
log(0.01), log(0.1), log(1), log(10) and log(100)
= -2, -1, 0, 1 and 2.
= -2, -1, 0, 1 and 2.


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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.
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 ==
== See also ==
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* [[Median]]
* [[Median]]
* [[Normal frequency distribution]]
* [[Normal frequency distribution]]

Revision as of 10:58, 22 August 2013

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