# 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

88 Related Articles

### 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.

### C. R. Rao

**Calyampudi Radhakrishna RaoC.R. RaoCR Rao**

### 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**

### Mathematical statistics

**mathematical statisticianstatistics mathematical statistics**

### Probabilistic number theory

**probabilistic**