Half-logistic distribution
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Probability density function |
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Cumulative distribution function |
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| Parameters | |
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| 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.
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[edit] Specification
[edit] 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,
[edit] 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,
[edit] 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).
