Jakob Bernoulli On the Law of Large Numbers Translated into English by Oscar Sheynin Berlin 2005

Probability and Statistics

1. Paevsky, V.V. Euler’s work in demography. In collected papers Leonard Euler. Moscow – Leningrad, 1935, pp. 103 – 110 ... 2. Bernoulli, D. On the mean duration of marriages, etc. (1768). Translated from Russian translation in Ptukha, M.V. (History of Statistics), vol. 1. Moscow, 1955, pp. 453 – 464... 3. Ondar, Kh.O. On the works of Davidov in probability theory and on his methodological view...

Studies in the History of Statistics and Probability Collected Translations Compiled and translated by Oscar Sheynin

Bortkiewicz’ Alleged Discovery: the Law of Small Numbers

Ladislaus von Bortkiewicz (1868 – 1931) published his law of small numbers (LSN) in 1898. The name of that law was unfortunate; moreover, lacking any mathematical expression, it was only a principle. Many commentators described it, but my paper is the first ever attempt to examine it thoroughly, and I argue that Kolmogorov’s unsubstantiated denial of its worth is correct. For a few decades the ...

A Note on the Strong Law of Large Numbers

Petrov (1996) proved the connection between general moment conditions and the applicability of the strong law of large numbers to a sequence of pairwise independent and identically distributed random variables. This note examines this connection to a sequence of pairwise negative quadrant dependent (NQD) and identically distributed random variables. As a consequence of the main theorem ...

1.1. Preliminary Remarks and the Integrals of the First Group …