The loglogistic distribution is a probability distribution whose logarithm has a logistic distribution. This distribution is often used in survival analysis to model events that experience an initial rate increase, followed by a rate decrease. It is also known as the Fisk distribution in economics applications.
The loglogistic distribution uses the following parameters.
|Mean of logarithmic values|
|Scale parameter of logarithmic values|
Probability Density Function
The probability density function (pdf) is
Relationship to Other Distributions
The loglogistic distribution is closely related to the logistic distribution. If x is distributed loglogistically with parameters μ and σ, then log(x) is distributed logistically with parameters μ and σ. The relationship is similar to that between the lognormal and normal distribution.