Accession Number : ADA187432

Title :   Asymptotic Expansions for Large Deviation Probabilities in the Strong Law of Large Numbers.

Descriptive Note : Technical rept.,

Corporate Author : STANFORD UNIV CA DEPT OF STATISTICS

Personal Author(s) : Fill, James A

PDF Url : ADA187432

Report Date : Oct 1987

Pagination or Media Count : 28

Abstract : Let X sub 1, X sub 2,...be a sequence of independent random variables with common distribution function F having zero mean, and let (S sub n) be the random walk of partial sums. The weak and strong laws of large numbers, respectively, imply that for any alpha epsilon IR and epsilon O the probabilities P(S sub m alpha + epsilon m) and P sub m = P(S sub n alpha + epsilon n for some n or = m) tend to 0 as m tends to infinity. Building upon work of Bahadur and Ranga Rao, The author produces complete asymptotic expansions for the probabilities P(S sub m alpha + epsilon m) and P sub m.

Descriptors :   *ASYMPTOTIC SERIES, *EXPANSION, PROBABILITY, RANDOM VARIABLES, NUMBERS, PROBABILITY DISTRIBUTION FUNCTIONS, NORMAL DENSITY FUNCTIONS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE