Logistic Distribution Calculator

About this calculator

The logistic distribution is a continuous probability distribution defined by a location parameter μ and scale parameter s, with probability density function f(x) = e^(−(x−μ)/s) / (s(1 + e^(−(x−μ)/s))²) and cumulative distribution function F(x) = 1 / (1 + e^(−(x−μ)/s)) — the same S-shaped sigmoid curve used as the activation function in logistic regression. Its mean equals μ, and its standard deviation equals s·π/√3.

Statisticians use the logistic distribution as the basis of logistic regression for modeling binary outcomes, and it also appears in growth modeling (population or adoption curves that saturate over time) and in neural networks, where the sigmoid function derived from its CDF is a classic activation function.