|Probability density function
|Cumulative distribution function
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
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,
- George, Olusengun; Meenakshi Devidas (1992). "Some Related Distributions". In N. Balakrishnan. Handbook of the Logistic Distribution. New York: Marcel Dekker, Inc. pp. 232–234. ISBN 0-8247-8587-8.
- Olapade, A.K. (February 2003). "On Characterizations of the Half-Logistic Distribution". InterStat, (2).