In probability theory and statistics, the logistic distribution is a continuous probability distribution. Its cumulative distribution function is the logistic function, which appears in logistic regression and feedforward neural networks.

The logistic distribution has longer tails than the normal distribution and a higher kurtosis of 1.2 (compared with 0 for the normal distribution). A related distribution is the half-logistic distribution.

f(x,mu,s) = exp(-(x-mu)/s)/(s(1+exp(-(x-mu)/s))^2)

where   

s = s/sqrt(3)/pi

support -Inf ⇐ x ⇐ Inf