Cramér

Cramér is a surname associated with Harald Cramér and with several mathematical concepts named after him. Harald Cramér (1893–1985) was a Swedish mathematician and statistician whose work helped shape modern probability theory and statistics. He introduced and developed results that bear his name in both probability and number theory.

Among his notable contributions are the Cramér–von Mises criterion, a family of statistics used to assess goodness of fit between an empirical distribution and a theoretical one, and the Cramér–Wold theorem, which states that a probability distribution on n-dimensional space is determined by its one-dimensional projections, a result central to convergence in distribution.

In the area of probability theory, Cramér's theorem provides a large deviations principle describing the exponential decay rate of probabilities for sums of independent and identically distributed random variables, with the rate function given by a Legendre transform of the cumulant generating function.

In number theory, Cramér conjectured that the gaps between consecutive primes are O((log p)^2); this prime gap conjecture remains unproven but has guided substantial research.

The name Cramér may also appear in other mathematical contexts named after different individuals, but Harald Cramér is the principal historical figure associated with the major theorems and conjectures bearing the name.