Über eine Eigenschaft der normalen Verteilungsfunktion

@article{Cramr1936berEE,
  title={{\"U}ber eine Eigenschaft der normalen Verteilungsfunktion},
  author={Harald Cram{\'e}r},
  journal={Mathematische Zeitschrift},
  year={1936},
  volume={41},
  pages={405-414}
}
  • H. Cramér
  • Published 1 December 1936
  • Mathematics
  • Mathematische Zeitschrift
Stability Problems in Cramér-Type Characterization in case of I.I.D. Summands
The stability property in Cramer's characterization of the normal law is considered in the case of identically distributed summands. As opposite results, instability is shown with respect to strong
Asymptotic Cram\'er type decomposition for Wiener and Wigner integrals
We investigate generalizations of the Cram\'er theorem. This theorem asserts that a Gaussian random variable can be decomposed into the sum of independent random variables if and only if they are
Asymptotic Cramér’s Theorem and Analysis on Wiener Space
We prove an asymptotic Cramer’s theorem, that is, if the sequence (X n + Y n ) n ≥ 1 converges in law to the standard normal distribution and for every n ≥ 1 the random variables X n and Y n are
Strong Decomposition of Random Variables
Abstract A random variable X is called strongly decomposable into (strong) components Y,Z, if X=Y+Z where Y=φ(X), Z=X−φ(X) are independent nondegenerate random variables and φ is a Borel function.
Symmetry and its discontents : essays on the history of inductive probability
Part I. Probability: 1. Symmetry and its discontents 2. The rule of succession 3. Buffon, Price, and Laplace: scientific attribution in the eighteenth century 4. W. E. Johnson's sufficientness
Maximum likelihood characterization of distributions
A famous characterization theorem due to C. F. Gauss states that the maximum likelihood estimator (MLE) of the parameter in a lo- cation family is the sample mean for all samples of all sample sizes
All sudden unexplained infant respiratory deaths may result from the same underlying mechanism
TLDR
Modeling data for age and/or gender distributions of SUDI/SUID and SIDS reported from the U.K., U.S., Norway and Germany indicates that the final mode of death for all SudI or SUID may be a consequence of different paths to the same biological phenomena as for SIDS, though the mechanism of death remains unclear.
Dissecting the spin distribution of dark matter haloes
The spin probability distribution of dark matter haloes has often been modelled as being very near to a lognormal. Most of the theoretical attempts to explain its origin and evolution invoke some
ON AN ANALYTICAL DECOMPOSITION OF THE POISSON
for all real t in a certain neighborhood of the point t = 0, where a2>0 and p are real numbers. Then each factor/n(/) is the characteristic function of a normal distribution. A similar analytical
...
1
2
3
4
5
...

References

SHOWING 1-6 OF 6 REFERENCES
Über den zentralen Grenzwertsatz der Wahrscheinlichkeitsrechnung
In einer fruheren Arbeit\(^1\)) wurde u. a. der Gultigkeitsbereich des klassischen Laplace-Ljapounoffschen Grenzwertsatzes genau abgegrenzt und es wurde ein Kriterium angegeben zur Feststellung, ob
Distribution functions and the Riemann zeta function
The present paper starts with a systematic study of distribution functions in ^-dimensional space and in particular of their infinite convolutions representing, in the language of the calculus of
On the Theory of Absolutely Additive Distribution Functions
Introduction. Recently * the author considered the problem of the asymptotic distribution of a movement in an n-space, e. g., the distribution of a complex-valued almost-periodic function (n = 2) . t
Sur les intégrales dont les éléments sont des variables aléatoires indépendantes
L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions