Logistic function

\(\operatorname{logistic}(x; L, k, x_0) = \displaystyle \frac{L}{1 + e^{-k(x + x_0)}}\)

• \(L\): The curve’s maximum value
• \(k\): the growth rate; the steepness of the curve
• \(x_0\): The \(x\) value of the sigmoid’s midpoint

(“Logistic Function” 2022)

Standard logistic function

\(\operatorname{logistic}(x)\) \(=\) \(\displaystyle \frac{1}{1 + e^{-x}}\) \(=\) \(\displaystyle \frac{e^x}{e^x + 1}\)

Bibliography

Backlinks

• Logit function