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Logit


The logit (/ˈlɪt/ LOH-jit) 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 p, the logit function gives the log-odds, or the logarithm of the odds p/(1 − p).

The logit of a number p between 0 and 1 is given by the formula:

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 is given by the inverse-logit:


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