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A probability distribution is strictly stable with index $\alpha$ if $n^{-1/\alpha }(T^{(1)}+\cdots +T^{(n)})\stackrel{d}{=}T$ for every positive integer $n$, for independent copies. Here no centering term is allowed, unlike in the general definition of a stable distribution.

A survival distribution is the probability distribution of an event or failure time, commonly summarized by its survivor function, hazard function or cumulative hazard function. It may contain atoms or a positive probability of an event never occurring; an ordinary density-based hazard therefore need not describe every survival distribution.

A transport-entropy inequality controls an optimal expected transportation cost between probability distributions by their Kullback-Leibler divergence.

If two random vectors have moment-generating functions that are finite and equal on a neighborhood of the origin, then they have the same probability distribution.

Variational inference approximates a posterior distribution by minimizing a Kullback-Leibler divergence over a chosen family of probability distributions. For an unnormalized posterior density $h$ and a trial probability density function $q$, minimizing ${\mathbb{E}}_q[\log q-\log h]$ is equivalent to minimizing $\mathrm{KL}(q\Vert h/\int h)$.

Wiener measure is the probability distribution of Brownian motion on a continuous-path space, usually $C_0([0,T])$ or $C_0([0,\infty ))$.