ON MASONS EXTENSION OF THE ERDOS RENYI LAW OF LARGE NUMBERS

• Type: Article in International Scientific Journal
• Date: 1991

Authors

BACRO, JN (Author) Other; BRITO, M (Author) FCUP

Journal

The Journal is awaiting validation by the Administrative Services.

Title: STATISTICS & PROBABILITY LETTERS

Vol. 11

Pages: 43-47

ISSN: 0167-7152

Indexing

ISI Web of Knowledge - 5 Citations

Scopus - 4 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-001-R9C

DOI: 10.1016/0167-7152(91)90175-q

Abstract (EN): Let S0 = 0 and S(n) = X1 + ... + X(n) denote the partial sums of an i.i.d. sequence of random variables with finite upper endpoint omega = sup{x:F(x) < 1}, where F(x) = P(X1 less-than-or-equal-to x). Let 1 less-than-or-equal-to k(n) less-than-or-equal-to n be a sequence such that c(n) = (log n)/k(n)-->infinity as n-->infinity, and consider U(n)(k(n)) = max0 less-than-or-equal-to i less-than-or-equal-to n - k(n)) (S(i) + k(n) - S(i)). In this paper, we show that the strong law U(n)(k(n))/(k(n)-gamma-(c(n)))-->1 as n-->infinity obtained by Mason (1989) for 0 < omega less-than-or-equal-to infinity remains valid under suitable assumptions for omega = 0. Here gamma-(.) is a function depending upon the distribution of X1.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 5