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The logistic distribution

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The logistic distribution has a similar shape to the normal distribution but has heavier tails.

 

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Distribution name

Logistic distribution

Common notation

Parameters

 = location parameter

 = scale parameter ()

Domain

Probability density function

where

Cumulative distribution function

Mean

Variance

Skewness

(Excess) kurtosis

Characteristic function

Other comments

The logistic distribution is sometimes called the sech-square(d) distribution because its pdf can also be expressed in terms of the hyperbolic secan function:

It should not then be confused with the hyperbolic secant distribution.

 

Nematrian web functions

 

Functions relating to the above distribution may be accessed via the Nematrian web function library by using a DistributionName of “logistic”. For details of other supported probability distributions see here.

 


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