Open Access
December, 1977 Reconstructing the Distribution from Partial Sums of Samples
G. Halasz, P. Major
Ann. Probab. 5(6): 987-998 (December, 1977). DOI: 10.1214/aop/1176995665


Let us observe an infinite sequence $z_1 = r_1 + \varepsilon_1, z_2 = r_2 + \varepsilon_2, \cdots$ where $r_1, r_2,\cdots$ are the partial sums of independent and identically distributed random variables and the sequence of random variables $\varepsilon_k$ (the errors) is bounded by a function $f(k)$. Knowing the sequence $z_n$ we want to determine the distribution function of the summands. We will show that this problem cannot be solved in general even if $f(k)$ is constant.


Download Citation

G. Halasz. P. Major. "Reconstructing the Distribution from Partial Sums of Samples." Ann. Probab. 5 (6) 987 - 998, December, 1977.


Published: December, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0372.60064
MathSciNet: MR451397
Digital Object Identifier: 10.1214/aop/1176995665

Primary: 60G50
Secondary: 42A80 , 62D05

Keywords: Cauchy's coefficient estimation , characteristic functions , mixing of distributions , partial sums of i.i.d. rv's

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 6 • December, 1977
Back to Top