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 →∞,
LL(\alpha, \beta) \to L(\alpha,\alpha/\beta).
  • 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.

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