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| {{Probability distribution|
| | Hi there, I am Alyson Pomerleau and I think it seems fairly great when you say it. Her family life in Ohio. Office supervising is what she does for a living. As a lady what she truly likes is fashion and she's been doing it for fairly a whilst.<br><br>Have a look at my site ... free psychic ([http://1.234.36.240/fxac/m001_2/7330 1.234.36.240]) |
| name =Half-logistic distribution|
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| type =density|
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| pdf_image =[[Image:Half-logistic distribution pdf.svg|325px|Probability density plots of half-logistic distribution]]|
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| cdf_image =[[Image:Half-logistic distribution cdf.svg|325px|Cumulative distribution plots of half-logistic distribution]]|
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| parameters =|
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| support =<math>k \in [0;\infty)\!</math>|
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| pdf =<math>\frac{2 e^{-k}}{(1+e^{-k})^2}\!</math>|
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| cdf =<math>\frac{1-e^{-k}}{1+e^{-k}}\!</math>|
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| mean =<math>\log_e(4)=1.386\ldots</math>|
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| median =<math>\log_e(3)=1.0986\ldots</math>|
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| mode =0|
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| variance =<math>\pi^2/3-(\log_e(4))^2=1.368\ldots</math>|
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| skewness =|
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| kurtosis =|
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| entropy =|
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| mgf =|
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| char =|
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| }}
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| 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
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| :<math>X = |Y| \!</math>
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| where ''Y'' is a logistic random variable, ''X'' is a half-logistic random variable.
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| == Specification ==
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| === Cumulative distribution function ===
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| 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'') = 2''F''(''k'') − 1 is the cdf of a half-logistic distribution. Specifically,
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| :<math>G(k) = \frac{1-e^{-k}}{1+e^{-k}} \mbox{ for } k\geq 0. \!</math>
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| === Probability density function ===
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| Similarly, the [[probability density function]] (pdf) of the half-logistic distribution is ''g''(''k'') = 2''f''(''k'') if ''f''(''k'') is the pdf of the logistic distribution. Explicitly,
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| :<math>g(k) = \frac{2 e^{-k}}{(1+e^{-k})^2} \mbox{ for } k\geq 0. \!</math>
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| ==References==
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| *{{cite book | last = George | first = Olusengun | coauthors = Meenakshi Devidas | editor = N. Balakrishnan | title = Handbook of the Logistic Distribution | year = 1992 | publisher = Marcel Dekker, Inc. | location = New York | pages = 232–234 | chapter = Some Related Distributions | isbn = 0-8247-8587-8}}
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| *{{cite journal | first = A.K. | last = Olapade |date=February 2003 | title = On Characterizations of the Half-Logistic Distribution | journal = InterStat, | issue = 2 | url = http://interstat.statjournals.net/YEAR/2003/articles/0302002.pdf}}
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| {{ProbDistributions|half-logistic distribution}}
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| [[Category:Continuous distributions]]
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| [[Category:Probability distributions]]
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