Of all the functional forms used for estimating the probabilities of a particular categorical outcome which optimize the fit by maximizing the likelihood function (e.g. [[Probit model|probit regression]], [[Poisson regression]], etc.), the logistic regression solution is unique in that it is a [[Maximum entropy probability distribution|maximum entropy]] solution.<ref name="Mount2011">{{cite web |urllast=http://wwwMount |first=J.win-vector.com/dfiles/LogisticRegressionMaxEnt.pdf |date=2011 |title=The Equivalence of Logistic Regression and Maximum Entropy models |last=Mount |firsturl=Jhttps://win-vector. |date=com/2011 |website= |publisher=/09/23/the-equivalence-of-logistic-regression-and-maximum-entropy-models/ |access-date=Feb 23, 2022 |website= |publisher= |quote=}}</ref> This is a case of a general property: an [[exponential family]] of distributions maximizes entropy, given an expected value. In the case of the logistic model, the logistic function is the [[natural parameter]] of the Bernoulli distribution (it is in "[[canonical form]]", and the logistic function is the canonical link function), while other sigmoid functions are non-canonical link functions; this underlies its mathematical elegance and ease of optimization. See {{slink|Exponential family|Maximum entropy derivation}} for details.
