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Mills ratio
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Mills ratio : ウィキペディア英語版
Mills ratio
In probability theory, the Mills ratio (or Mills's ratio〔) of a continuous random variable X is the function
: m(x) := \frac ,
where f(x) is the probability density function, and
:\bar(x) := \Pr() = \int_x^ f(u)\, du
is the complementary cumulative distribution function (also called survival function). The concept is named after John P. Mills. The Mills ratio is related〔 to the hazard rate ''h''(''x'') which is defined as
:h(x):=\lim_ \frac\Pr(< X \leq x + \delta | X > x )
by
:m(x) = \frac.
==Example==

If X has standard normal distribution then
:m(x) \sim 1/x , \,
where the sign \sim means that the quotient of the two functions converges to 1 as x\to+\infty. More precise asymptotics can be given.〔

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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