“Half-logistic distribution”的意思、由来-开放百科全书

词条

Half-logistic distribution

释义

Specification
Cumulative distribution function Probability density function
References

{{Probability distribution|

  name       =Half-logistic distribution|  type       =density|  pdf_image  =|  cdf_image  =|  parameters =|  support    =|  pdf        =|  cdf        =|  mean       =|  median     =|  mode       =0|  variance   =|  skewness   =|  kurtosis   =|  entropy    =|  mgf        =|  char       =|

}}

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

{{cite book|last1=Johnson|first1=N. L.|last2=Kotz|first2=S.|last3=Balakrishnan|first3=N.|title=Continuous univariate distributions|edition=2nd|volume=2|publisher=Wiley|place=New York|year=1994|chapter=23.11|page=150}}
{{cite book | last = George | first = Olusegun |author2=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}}
{{citation | last = Olapade | first = A.K. | year=2003 | title = On characterizations of the half-logistic distribution | journal = InterStat | volume=2003 | issue = February | page=2 | url = http://interstat.statjournals.net/YEAR/2003/articles/0302002.pdf | issn=1941-689X }}

1 : Continuous distributions

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