On the central limit theorem in the case of not equally distributed random variables

1949/01/01 by Harald Bergström · 4 citations
Decision Sciences · Computer Science · Physics and Astronomy · #Probability and Risk Models #Neural Networks and Applications #Scientific Research and Discoveries

paper · doi:10.1080/03461238.1949.10419757

openalex publication_date 1949/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

1. Introduction. In two earlier papers 1 Bergström H., On the Central Limit Theorem, Skandinavisk Aktuarietidskrift 1944, p. 139, and On the Central Limit Theorem in the Space Rk , k > 1, Skandinavisk Aktuarietidskrift 1946, p. 108. In the following they are denoted veith C. L. T. I and C. L. T. II respectively. I have studied the difference between the d. f. of a sum of n equally distributed random variables and a corresponding normal d. f. I also remarked that my method could be used for not equally distributed variables. As this case presents some new aspects I will treat it here.

Citations

• On the central limit theorem in the spaceRk,k> 1.
• On the central limit theorem

Cited by

• A sharpening of the inequality of Berry-Esseen
• Refinement of the upper bound of the constant in the central limit theorem
• On the Upper Bound for the Absolute Constant in the Berry–Esseen Inequality
• Harald Bergström [wikipedia]