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# Log-Logistic Random Variable Generator

The log-logistic distribution, also known as the Fisk distribution in economics, is a two-parameter probability distribution. The parameter *a* governs the shape, while *b* is a scaling factor. If a random variable *X* has a logistic distribution, then ln(*X*) has a log-logistic distribution. The Fisk probability model has a wide variety of applications, including, hydrology, survival analysis, and wealth distribution. You can use the calculator below to generate random numbers from a log-logistic distribution.

The log-logistic probability density function is

*b*. The mean, mode, variance, and skewness are more complicated functions of

*a*and

*b*:

*b*(1/3)

^{1/a}and

*b*(3)

^{1/a}respectively.

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