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The lognormal distribution

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Distribution name

Lognormal distribution

Common notation

Parameters

 = scale parameter ()

 = location parameter

Domain

Probability density function

Cumulative distribution function

Mean

Variance

Skewness

(Excess) kurtosis

Characteristic function

No simple expression that is not divergent

Other comments

The median of a lognormal distribution is  and its mode is .

 

The truncated moments of   are:

 

Nematrian web functions

 

Functions relating to the above distribution may be accessed via the Nematrian web function library by using a DistributionName of “lognormal”. Functions relating to a generalised version of this distribution including additional location (i.e. shift) and scale parameters may be accessed by using a DistributionName of “lognormal4” ”, see also including additional shift and scale parameters. For details of other supported probability distributions see here.

 


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