A moment inequality with an application to the central limit theorem
- 1 July 1956
- journal article
- research article
- Published by Taylor & Francis in Scandinavian Actuarial Journal
- Vol. 1956 (2) , 160-170
- https://doi.org/10.1080/03461238.1956.10414946
Abstract
Consider a sequence of independent random variables (r.v.) X 1 X 2, …, Xn , … , with the same distribution function (d.f.) F(x). Let E (Xn ) = 0, E , E (ϕ(X)) denoting the mean value of the r.v. ϕ (X). Further, let the r.v. where have the d.f. F n (x). It was proved by Berry [1] and the present author (Esseen [2], [4]) that Φ(x) being the normal d.f.Keywords
This publication has 2 references indexed in Scilit:
- Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian lawActa Mathematica, 1945
- The accuracy of the Gaussian approximation to the sum of independent variatesTransactions of the American Mathematical Society, 1941