Logistic Distribution

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.
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The Logistic distribution has density function:
f(x) = (1/b)*e-(x-a)/b * [1+e-(x-a)/b]-2
where
a is the mean of the distribution
b is the scale parameter
e is the base of the natural logarithm, sometimes called Euler's e (2.71...)
Logistic Distribution (animation) 
The graphic above shows the changing shape of the Logistic distribution when the location parameter equals 0 and the scale parameter equals 1, 2, and 3.