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Talk:Logistic distribution/Generalized log-logistic distribution

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Generalized log-logistic distribution

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The Generalized log-logistic distribution (GLL) has three parameters and .

Generalized log-logistic
Parameters

location (real)
scale (real)

shape (real)
Support


PDF


where
CDF


where
Mean


where
Median
Mode
Variance


where

The cumulative distribution function is

for , where is the location parameter, the scale parameter and the shape parameter. Note that some references give the "shape parameter" as .


The probability density function is


again, for