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. | ||
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: | ||
0.01, 0.1, 1, 10 and 100. | 0.01, 0.1, 1, 10 and 100. | ||
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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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. | ||
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. | ||
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]] | ||
[[Category:The_business_context]] | |||
Latest revision as of 17:56, 1 July 2022
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.
