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logit : ウィキペディア英語版
logit

The logit ( ) function is the inverse of the sigmoidal "logistic" function or logistic transform used in mathematics, especially in statistics. When the function's parameter represents a probability , the logit function gives the log-odds, or the logarithm of the odds .〔(【引用サイトリンク】title=LOG ODDS RATIO )
==Definition==

The logit of a number ''p'' between 0 and 1 is given by the formula:
:\operatorname(p)=\log\left( \frac \right) =\log(p)-\log(1-p)=-\log\left( \frac - 1\right). \!\,
The base of the logarithm function used is of little importance in the present article, as long as it is greater than 1, but the natural logarithm with base e is the one most often used. The choice of base corresponds to the choice of logarithmic unit for the value: base 2 corresponds to a bit, base e to a nat, and base 10 to a ban (dit, hartley); these units are particularly used in information-theoretic interpretations. For each choice of base, the logit function takes values between negative and positive infinity.
The "logistic" function of any number \alpha is given by the inverse-logit:
:\operatorname^(\alpha) = \frac = \frac
If ''p'' is a probability, then ''p''/(1 − ''p'') is the corresponding odds; the logit of the probability is the logarithm of the odds. Similarly, the difference between the logits of two probabilities is the logarithm of the odds ratio (''R''), thus providing a shorthand for writing the correct combination of odds ratios only by adding and subtracting:
:\operatorname(R)=\log\left( \frac/(1-p_1)}/(1-p_2)} \right) =\log\left( \frac \right) - \log\left(\frac\right)=\operatorname(p_1)-\operatorname(p_2). \!\,

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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