Quantum theory essentially replaces classically accurate values by a probabilistic distribution that can be formulated using, e.g., a wavefunction, a density matrix, or a phase-space distribution. Conceptually, there is always, at least formally, probability distribution behind each observable that is measured. Already in 1889, a long time before quantum physics was formulated, Thorvald N. Thiele proposed the cumulants that describe probabilistic distributions with as few quantities as possible; he called them half-invariants. The cumulants form a sequence of quantities such as mean, variance, skewness, kurtosis, and so on, that identify the distribution with increasing accuracy as more cumulants are used.