Log-logistic Distribution - Related Distributions

Related Distributions

• If then
• (Dagum distribution)
• (Singh-Maddala distribution)
• Beta prime distribution

• If X has a log-logistic distribution with scale parameter and shape parameter then Y = log(X) has a logistic distribution with location parameter and scale parameter .

• As the shape parameter of the log-logistic distribution increases, its shape increasingly resembles that of a (very narrow) logistic distribution. Informally, as →∞,

• The log-logistic distribution with shape parameter and scale parameter is the same as the generalized Pareto distribution with location parameter, shape parameter and scale parameter

• The addition of another parameter (a shift parameter) formally results in a shifted log-logistic distribution, but this is usually considered in a different parameterization so that the distribution can be bounded above or bounded below.