Half-logistic distribution
Probability density function
Cumulative distribution function
Support	${\displaystyle k\in [0;\mathrm{\infty })}$
PDF	${\displaystyle \frac{2e^{-k}}{(1+e^{-k}{)}^2}}$
CDF	${\displaystyle \frac{1-e^{-k}}{1+e^{-k}}}$
Mean	${\displaystyle \ln (4)=1.386\dots }$
Median	${\displaystyle \ln (3)=1.0986\dots }$
Mode	0
Variance	${\displaystyle {\pi }^2/3-(\ln (4){)}^2=1.368\dots }$
Entropy	${\displaystyle \log \left(\frac{e^2}{2}\right)}$

Inprobability theory andstatistics, thehalf-logistic distribution is a continuousprobability distribution—the distribution of the absolute value of arandom variable following thelogistic distribution. That is, for

${\displaystyle X=|Y|}$

whereY is a logistic random variable,X is a half-logistic random variable.

Thecumulative distribution function (cdf) of the half-logistic distribution is intimately related to the cdf of the logistic distribution. Formally, ifF(k) is the cdf for the logistic distribution, thenG(k) = 2F(k) − 1 is the cdf of a half-logistic distribution. Specifically,

${\displaystyle G(k)=\frac{1-e^{-k}}{1+e^{-k}}\text{ for }k\ge 0.}$

Similarly, theprobability density function (pdf) of the half-logistic distribution isg(k) = 2f(k) iff(k) is the pdf of the logistic distribution. Explicitly,

${\displaystyle g(k)=\frac{2e^{-k}}{(1+e^{-k}{)}^2}\text{ for }k\ge 0.}$

• Johnson, N. L.; Kotz, S.; Balakrishnan, N. (1994). "23.11".Continuous univariate distributions. Vol. 2 (2nd ed.). New York: Wiley. p. 150.
• George, Olusegun; Meenakshi Devidas (1992). "Some Related Distributions". In N. Balakrishnan (ed.).Handbook of the Logistic Distribution. New York: Marcel Dekker, Inc. pp. 232–234.ISBN 0-8247-8587-8.
• Olapade, A.K. (2003),"On characterizations of the half-logistic distribution"(PDF),InterStat,2003 (February): 2,ISSN 1941-689X

• Continuous distributions

• Articles with short description
• Short description matches Wikidata