How do I create a function to generate log-logistic distribution?

I need to create a function (in Mathematica) to generate a log-logistic distribution (also called a Fisk distribution). I know the log-logistic distribution is derived from the logistic distribution, as follows:

X = Random variable with logistic distribution
Y = e^X = Random variable with log-logistic distribution

and I I found formulas, which will generate a PDF or CDF directly, but I think I want something more fundamental such as a LoglogisticDistribution[&] function which I could use like any of Mathematica's native distribution functions like:

NormalDistribution[], LogNormalDistribution[], GammaDistribution[], ...

In situations like this::

PDF[LoglogisticDistribution[x] , y]
CDF[LoglogisticDistribution[x] , y]

Pseudo code or almost any other code will do, I can translate into Mathematica.

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AlphaSquaredAuthor Commented:

I've seen the link you reference, but I don't think it gives me what I need, it tells me how to calculate a PDF, CDF, moments, et al.  I think I need something more basic.  

I have legacy code in which I can reference any distribution so I need to develop an equivalent for log-logistic to normal distribution or Welbull distribution or any other of Mathematica's built in distributions.  that way I won't have to recreate a bunch of functions to deal with me only being able to generate a PDF or CDF of a log-logistic distribution (or any other native Mathematica funnction that can manipulate distributions)..

ICan I work backwards from a PDF or CDF of the distribution to the distribution itself?
You can generate X = Random variable with logistic distribution
Z = Random variable with uniform distribution
X = log(Z/(1-Z))
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