Harald Cramér

CramérHarald CramerCramér, HaraldH. Cramér
Harald Cramér (25 September 1893 – 5 October 1985) was a Swedish mathematician, actuary, and statistician, specializing in mathematical statistics and probabilistic number theory.wikipedia
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Cramér's conjecture

conjecturedCramer conjectureCramér conjecture
His most famous paper on this subject is entitled "On the order of magnitude of the difference between consecutive prime numbers", which provided a rigorous account of the constructive role in which probability applied to number theory and included an estimate for prime gaps that became known as Cramér's conjecture.
In number theory, Cramér's conjecture, formulated by the Swedish mathematician Harald Cramér in 1936, is an estimate for the size of gaps between consecutive prime numbers: intuitively, that gaps between consecutive primes are always small, and the conjecture quantifies asymptotically just how small they must be.

Actuary

actuariesactuarialactuarial analysis
Harald Cramér (25 September 1893 – 5 October 1985) was a Swedish mathematician, actuary, and statistician, specializing in mathematical statistics and probabilistic number theory.

List of Fellows of the American Statistical Association

Fellow of the American Statistical AssociationFellowFellows
In 1950 he was elected as a Fellow of the American Statistical Association.

Marcel Riesz

RieszRiesz MarcelRiesz, Marcel
He eventually began his work on his doctoral studies in mathematics which were supervised by Marcel Riesz at the University of Stockholm.
Riesz's doctoral students in Stockholm include Harald Cramér and Einar Carl Hille.

Herman Wold

Wold, HermanHerman Ole Andreas WoldH. Wold
During his tenure at Stockholm University, Cramér was a PhD advisor for 10 students, most notably Herman Wold and Kai Lai Chung.
It was an opportune time, for Harald Cramér had been appointed Professor of Actuarial Mathematics and Mathematical Statistics.

Chung Kai-lai

Kai Lai ChungKai-Lai ChungKai-lai, Chung
During his tenure at Stockholm University, Cramér was a PhD advisor for 10 students, most notably Herman Wold and Kai Lai Chung.
Chung's dissertation was titled “On the maximum partial sum of sequences of independent random variables” and was under the supervision of John Wilder Tukey and Harald Cramér.

Prime gap

prime gapsgapgaps
His most famous paper on this subject is entitled "On the order of magnitude of the difference between consecutive prime numbers", which provided a rigorous account of the constructive role in which probability applied to number theory and included an estimate for prime gaps that became known as Cramér's conjecture.
Harald Cramér proved that the Riemann hypothesis implies the gap g n satisfies

Cramér–Rao bound

Cramér–Rao inequalityCramér–Rao lower bound
This term is named in honor of Harald Cramér, Calyampudi Radhakrishna Rao, Maurice Fréchet and Georges Darmois all of whom independently derived this limit to statistical precision in the 1940s.

Large deviations theory

large deviationsLarge deviation theorytheory of large deviations
While some basic ideas of the theory can be traced to Laplace, the formalization started with insurance mathematics, namely ruin theory with Cramér and Lundberg.

Rate function

large deviation principleCramér functiongood rate function
A rate function is also called a Cramér function, after the Swedish probabilist Harald Cramér.

Guy Medal

Guy Medal in BronzeGuy Medal in SilverGuy Medal in Gold

Cramér's V

Cramer's VV
It is based on Pearson's chi-squared statistic and was published by Harald Cramér in 1946.

Ruin theory

risk theoryruin problemrisk of ruin
He was also known for his pioneering efforts in insurance risk theory.
Lundberg's work was republished in the 1930s by Harald Cramér.

Ulf Grenander

Grenander UlfGrenander, Ulf
Grenander earned his Ph.D. at Stockholm University in 1950 under the supervision of Harald Cramér.

Cramér–Wold theorem

The theorem is named after Harald Cramér and Herman Ole Andreas Wold.

Cramér–von Mises criterion

Cramér–von Mises statisticCramér–von Mises statisticsCramér–von Mises test
The criterion is named after Harald Cramér and Richard Edler von Mises who first proposed it in 1928–1930.

Cramér's theorem (large deviations)

Cramér's large deviation theoremCramér's theorem
A weak version of this result was first shown by Harald Cramér in 1938.

Cramér’s decomposition theorem

Cramér's theoremCramer's decomposition theorem
The latter result, initially announced by Paul Lévy, has been proved by Harald Cramér.

Hermite polynomials

Hermite polynomialHermiteHermite functions
For real x, the Hermite functions satisfy the following bound due to Harald Cramér and Jack Indritz:

Sweden

SwedishSWEKingdom of Sweden
Harald Cramér (25 September 1893 – 5 October 1985) was a Swedish mathematician, actuary, and statistician, specializing in mathematical statistics and probabilistic number theory.

Mathematician

mathematiciansapplied mathematicianMathematics
Harald Cramér (25 September 1893 – 5 October 1985) was a Swedish mathematician, actuary, and statistician, specializing in mathematical statistics and probabilistic number theory.

Statistician

statisticiansStatistical theoristsstatistical analyst
Harald Cramér (25 September 1893 – 5 October 1985) was a Swedish mathematician, actuary, and statistician, specializing in mathematical statistics and probabilistic number theory.

Mathematical statistics

mathematical statisticianstatistics mathematical statistics
Harald Cramér (25 September 1893 – 5 October 1985) was a Swedish mathematician, actuary, and statistician, specializing in mathematical statistics and probabilistic number theory.

Probabilistic number theory

probabilistic
Harald Cramér (25 September 1893 – 5 October 1985) was a Swedish mathematician, actuary, and statistician, specializing in mathematical statistics and probabilistic number theory.