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The log-logistic distribution

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Distribution name

Log-logistic distribution

Common notation

Parameters

 = scale parameter ()

 = shape parameter ()

Domain

Probability density function

Cumulative distribution function

Mean

where  and  is the cosecant function

Variance

Other comments

Is also called the Fisk distribution. Its non-central moments are (if :

 

Nematrian web functions

 

Functions relating to the above distribution may be accessed via the Nematrian web function library by using a DistributionName of “loglogistic”. Functions relating to a generalised version of this distribution including an additional location (i.e. shift) parameter may be accessed by using a DistributionName of “loglogistic3”, see also including additional shift and scale parameters. For details of other supported probability distributions see here.

 


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