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Logit-normal distribution : ウィキペディア英語版
Logit-normal distribution
\, e^}\frac
| cdf = \frac12\Big(+ \operatorname\Big( \frac}
In probability theory, a logit-normal distribution is a probability distribution of a random variable whose logit has a normal distribution. If ''Y'' is a random variable with a normal distribution, and ''P'' is the logistic function, then ''X'' = ''P''(''Y'') has a logit-normal distribution; likewise, if ''X'' is logit-normally distributed, then ''Y'' = logit(''X'')= log (''X''/(1-''X'')) is normally distributed. It is also known as the logistic normal distribution,〔J Atchison and SM Shen. "Logistic-normal distributions: Some properties and uses." Biometrika, 1980. (Google Scholar link )〕 which often refers to a multinomial logit version (e.g.〔http://people.csail.mit.edu/tomasz/papers/huang_hln_tech_report_2006.pdf〕〔Peter Hoff, 2003. (Link )〕〔http://www.springerreference.com/docs/html/chapterdbid/205424.html〕〔http://brenocon.com/blog/2011/05/log-normal-and-logistic-normal-terminology/〕).
A variable might be modeled as logit-normal if it is a proportion, which is bounded by zero and one, and where values of zero and one never occur.
== Characterization ==


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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