imported>Doug Williamson |
imported>Doug Williamson |
| Line 1: |
Line 1: |
| A lognormal distribution is one where the logarithm - for example log(X) or ln(X) - of the variable is normally distributed.
| | The risk of loss arising from the need to replace a contract before having paid away the principal amount. |
|
| |
|
| Lognormal distributions have a minimum - usually 'worst case' - value, whilst having an infinitely high upside.
| | Often quantified approximately as the expected profit foregone. |
| | |
| 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 == | | == See also == |
| * [[Frequency distribution]] | | * [[Credit risk]] |
| * [[Leptokurtic frequency distribution]] | | * [[Principal risk]] |
| * [[Lognormally distributed share returns]]
| |
| * [[Median]]
| |
| * [[Normal frequency distribution]]
| |
| | |
| [[Category:The_business_context]]
| |
