Английская Википедия:Half-logistic distribution

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Шаблон:Probability distribution{(1+e^{-k})^2}\!</math>|

 cdf        =<math>\frac{1-e^{-k}}{1+e^{-k}}\!</math>|
 mean       =<math>\log_e(4)=1.386\ldots</math>|
 median     =<math>\log_e(3)=1.0986\ldots</math>|
 mode       =0|
 variance   =<math>\pi^2/3-(\log_e(4))^2=1.368\ldots</math>|
 skewness   =|
 kurtosis   =|
 entropy    =|
 mgf        =|
 char       =|

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In probability theory and statistics, the half-logistic distribution is a continuous probability distribution—the distribution of the absolute value of a random variable following the logistic distribution. That is, for

<math>X = |Y| \!</math>

where Y is a logistic random variable, X is a half-logistic random variable.

Specification

Cumulative distribution function

The cumulative distribution function (cdf) of the half-logistic distribution is intimately related to the cdf of the logistic distribution. Formally, if F(k) is the cdf for the logistic distribution, then G(k) = 2F(k) − 1 is the cdf of a half-logistic distribution. Specifically,

<math>G(k) = \frac{1-e^{-k}}{1+e^{-k}} \text{ for } k\geq 0. \!</math>

Probability density function

Similarly, the probability density function (pdf) of the half-logistic distribution is g(k) = 2f(k) if f(k) is the pdf of the logistic distribution. Explicitly,

<math>g(k) = \frac{2 e^{-k}}{(1+e^{-k})^2} \text{ for } k\geq 0. \!</math>

References

• Шаблон:Cite book
• Шаблон:Cite book
• Шаблон:Citation