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Loglogistic Distribution

Overview

The loglogistic distribution is a probability distribution whose logarith 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.

Parameters

The loglogistic distribution uses the following parameters.

ParameterDescriptionSupport
muLog mean
sigmaLog scale parameter

Probability Density Function

The probability density function (pdf) is

where .

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 mean and standard deviation. The relationship is similar to that between the lognormal and normal distribution.

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