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Inverse Mills ratio
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Inverse Mills ratio : ウィキペディア英語版
Inverse Mills ratio
In statistics, the inverse Mills ratio, named after John P. Mills, is the ratio of the probability density function to the cumulative distribution function of a distribution.
==Uses==

Use of the inverse Mills ratio is often motivated by the following property of the truncated normal distribution. If ''X'' is a random variable having a normal distribution with mean ''μ'' and variance ''σ''2, then
: \begin
& \operatorname(X > \alpha \, ) =
\mu + \sigma \frac \big)}\big)}, \\
& \operatorname(X < \alpha \, ) =
\mu + \sigma \frac \big)}\big)},
\end
where ''α'' is a constant, ''ϕ'' denotes the standard normal density function, and ''Φ'' is the standard normal cumulative distribution function. The two fractions are the inverse Mills ratios.

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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