Logit

In statistics, the logit (logistic unit) or log-odds function is the quantile function associated with the standard logistic distribution. It has many uses in data analysis and machine learning, especially in data transformations. Mathematically, the logit is the inverse of the standard logistic function ⁠ σ ( x ) = 1 / ( 1 + e − x ) {\displaystyle \textstyle \sigma (x)=1/(1+e^{-x})} ⁠, so the logit is defined as logit ⁡ p = σ − 1 ( p ) = ln ⁡ p 1 − p for p ∈ ( 0 , 1 ) . {\displaystyle \operatorname {logit} p=\sigma ^{-1}(p)=\ln {\frac {p}{1-p}}\quad {\text{for}}\quad p\in (0,1).} Because of this, the logit is also called the log-odds since it is equal to the logarithm of the odds p 1 − p {\textstyle {\frac {p}{1-p}}} where p is a probability. Thus, the logit is a type of function that maps probability values from ( 0 , 1 ) {\displaystyle (0,1)} to real numbers in ⁠ ( − ∞ , + ∞ ) {\displaystyle (-\infty ,+\infty )} ⁠, akin to the probit function.