The log-logistic distribution
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![[SmartChart]](I/LogLogisticDistribution_files/image001.gif)
![[SmartChart]](I/LogLogisticDistribution_files/image002.gif)
![[SmartChart]](I/LogLogisticDistribution_files/image003.gif)
 
 
  | 
   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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