Dirichlet's contributions to mathematical probability theory
type: Item
instance of: scholarly article
title: Dirichlet's contributions to mathematical probability theory
zbMATH Open document ID: 0795.01007
author: Hans Fischer
published in: Historia Mathematica
publication date: 1994-09-11T00:00:00Z
review text: The author mainly describes Dirichlet's unpublished courses on probability theory (1838-1846) which the latter began delivering in 1829. Dirichlet did not study either the ``moral'' applications of probability or its philosophical aspects and, while discussing the method of least squares, neglected its substantiations made by Gauss. Dirichlet based his course on the integral calculus and, in proving the central limit theorem, presented it more rigorously than Chebyshev did in 1879/1880. However, the author does not remark that 1) Chebyshev himself noted that his derivation was not rigorous or that 2) later on (1887) he offered a much better substantiation.
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 60-03
zbMATH DE Number: 567607
zbMATH Keywords: central limit theorem
zbMATH Keywords: Chebyshev
zbMATH Keywords: method of least squares
reviewed by: O. B. Sheĭnin
MaRDI profile type: Publication
full work available at URL: hmat.1994.1007
OpenAlex ID: W2081002437
Wikidata QID: Q56172757
cites work: Q3253775
cites work: Q3953731
cites work: Q3799981
cites work: Q4091266
cites work: Q3042203
cites work: Q3709583
cites work: Q4146703
cites work: Q4883236
cites work: Q3689153
cites work: Clausius' erste Anwendung der Wahrscheinlichkeitsrechnung im Rahmen der atmosphärischen Lichtstreuung
cites work: Rudolph Clausius' Beitrag zur Einführung wahrscheinlichkeitstheoretischer Methoden in die Physik der Gase nach 1856
cites work: The three parts of the Dirichlet Nachlaß
cites work: Finite random sums. (A historical essay.)
cites work: P.S. Laplace's work on probability
cites work: Laplace's theory of errors
cites work: C. F. Gauss and the theory of errors
cites work: On the history of medical statistics
cites work: Q4773996
cites work: Simon Newcomb, Percy Daniell, and the History of Robust Estimation 1885-1920
cites work: Q3803965
DOI: 10.1006/HMAT.1994.1007
description: scientific article; zbMATH DE number 567607