It resembles the normal distribution in shape but has heavier tails (higher kurtosis).

In this equation μ is the mean, and s is a scale parameter proportional to the standard deviation.

They are defined as follows: An alternative parameterization of the logistic distribution can be derived by expressing the scale parameter,

One of the most common applications is in logistic regression, which is used for modeling categorical dependent variables (e.g., yes-no choices or a choice of 3 or 4 possibilities), much as standard linear regression is used for modeling continuous variables (e.g., income or population).

This phrasing is common in the theory of discrete choice models, where the logistic distribution plays the same role in logistic regression as the normal distribution does in probit regression.

Those energy levels whose energies are closest to the distribution's "mean" (Fermi level) dominate processes such as electronic conduction, with some smearing induced by temperature.

[4] In hydrology the distribution of long duration river discharge and rainfall (e.g., monthly and yearly totals, consisting of the sum of 30 respectively 360 daily values) is often thought to be almost normal according to the central limit theorem.

The blue picture illustrates an example of fitting the logistic distribution to ranked October rainfalls—that are almost normally distributed—and it shows the 90% confidence belt based on the binomial distribution.

The rainfall data are represented by plotting positions as part of the cumulative frequency analysis.

The United States Chess Federation and FIDE have switched its formula for calculating chess ratings from the normal distribution to the logistic distribution; see the article on Elo rating system (itself based on the normal distribution).