Helmert's work in the theory of errors

@article{Sheynin1995HelmertsWI,
  title={Helmert's work in the theory of errors},
  author={Oscar Sheynin},
  journal={Archive for History of Exact Sciences},
  year={1995},
  volume={49},
  pages={73-104}
}
  • O. Sheynin
  • Published 1 March 1995
  • Mathematics
  • Archive for History of Exact Sciences
Les travaux de Helmert (F.R.) sont decrits afin de comprendre la theorie des erreurs en statistiques 
View on Springer
33 Citations
Background Citations
5
Methods Citations
4

33 Citations

Citation Type

Citation Type

Studies in the history of probability and statistics XLIV A forerunner of the t-distribution
SUMMARY The t-distribution first occurred in a paper by Ltiroth (1876) on the classical theory of errors in connection with a Bayesian result.
The Distribution of the Sample Variance Under Normality
The article translated here is actually just one part, with its own title, of a three-part paper that slays several dragons (Helmert, 1876b). Let X 1,..., X n be independent N(µ, σ 2) variates. In…
Friedrich Robert Helmert in memory of his 100th year of death
The presentation starts with the description of Helmert’s course of life and deals in the second and third part with his main research fields, namely adjustment theory and geodesy. It concludes with…
C.F. Gauss and the method of least squares
Gauss introduced the MLSq and Helmert completed its development whereas Bessel made important discoveries in astronomy and geodesy but was often extremely inattentive. Gauss’ final condition of least…
two essays on the history of the theory of errors
TLDR
These essays extract two threads from the complicated history of the theory of errors in the 19th and early 20th centuries: the Gauss-Dedekind-Luroth line produced Bayesian analysis for the normal regression model while the Fisher line developed sampling theory analysis.
Early sample measures of variability
This paper attempts a brief account of the history of sample measures of dispersion, with major emphasis on early developments. The statistics considered include standard deviation, mean deviation,…
The First Problem of Probabilistic Regression: The Bias Problem
Minimum Bias solution of problems with datum defects. LUMBE of fixed effects. The bias problem in probabilistic regression has been the subject of Sect. 437 for simultaneous determination of first…
On Student's 1908 Article “The Probable Error of a Mean”
This month marks the 100th anniversary of the appearance of William Sealey Gosset's celebrated article, “The Probable Error of a Mean” (Student 1908a). Gosset's elegant result represented the first…
Student's t-Distribution versus Zeldovich-Kompaneets Solution of Diffusion Problem
Student’s t-distribution is compared to a solution of superdiffusion equation. This t-distribution is a continuous probability distribution that arises in the problem of estimating the mean of a…
Anderson's Forgotten Obituary of von Bortkiewicz
Ladislaus von Bortkiewicz, einer polnischen Familile entstammend, wurde 1868 in Petersburg geboren. Seine akademische Laufbahn führte ihn über die Universitäten Göttingen und Straßburg an die…
...
1
2
3
4
...

References

SHOWING 1-10 OF 30 REFERENCES
Origin of the Theory of Errors
J. H. LAMBERT should be given precedence over Gauss as the originator of the theory of errors. Galle1 stated that Gauss arrived at the idea of the principle of least squares while reading Lambert,…
C. F. Gauss and geodetic observations
Ayant etudie les travaux de Gauss sur la theorie de l'erreur, l'A. etudie une methode d'estimation de l'erreur basee sur l'etude des statistiques mathematiques
Gauss's first argument for least squares
Gauss first published an argument for the law of least squares in the Theoria Motus of 1809, though he had been using the law for some time.1 His argument there was influential throughout the…
Laplace's theory of errors
The genesis and development of the theory of errors before Laplace have been considered in a series of my articles [69] -[74]. My present aim is to elucidate the relevant work of Laplace himself,…
Notes on the method of least squares
In inferring the value of a physical quantity x from observations some risk must be accepted. It is therefore presumed that the investigator has made up his mind how much risk he will take, and…
Two Theories of Experimental Error
  • A. Colclough
  • Philosophy
    Journal of Research of the National Bureau of Standards
  • 1987
The reader … will have seized my meaning if he perceives that the different situations in which uncertain inferences may be attempted admit of logical distinctions which should guide our…
On V. Ya. Buniakovsky's work in the theory of probability
C.F. Gauss and the theory of errors
Early history of the theory of probability
  • O. Sheynin
  • Economics
    Archive for history of exact sciences
  • 1977
FORERUNNERS OF THE PEARSON χ2
...
1
2
3
...