Half-logistic distribution

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

Half-logistic distribution
Probability density function
Cumulative distribution function
Mode 0

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


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,

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,


  • Johnson, N. L.; Kotz, S.; Balakrishnan, N. (1994). "23.11". Continuous univariate distributions. 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
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