Half-logistic distribution: Information from Answers.com

Half-logistic distribution

Probability density function
Cumulative distribution function
Parameters
Support
Probability density function (pdf)
Cumulative distribution function (cdf)
Mean
Median
Mode	0
Variance
Skewness
Excess kurtosis
Entropy
Moment-generating function (mgf)
Characteristic 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.

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,

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,

References

• George, Olusengun; Meenakshi Devidas (1992). "Some Related Distributions", in N. Balakrishnan: Handbook of the Logistic Distribution. New York: Marcel Dekker, Inc., 232–234. ISBN 0-8247-8587-8.

• Olapade, A.K. (February 2003). "On Characterizations of the Half-Logistic Distribution". InterStat, (2), http://interstat.statjournals.net/YEAR/2003/articles/0302002.pdf.