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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