Contents

Logistic Distribution

Overview

The logistic distribution is used for growth models and in logistic regression. It has longer tails and a higher kurtosis than the normal distribution.

Parameters

The logistic distribution uses the following parameters.

ParameterDescriptionSupport
muMean<μ<
sigmaScale parameterσ0

Probability Density Function

The probability density function (pdf) is

f(x|μ,σ)=exp{xμσ}σ(1+exp{xμσ})2;<x<.

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.

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