A Note on Some Probability Inequalities for Sample Sums and Their Applications.

Abstract

Let S sub n denote the partial sums of iid random variables with mean zero and moment generating function existing in some neighbourhood of the origin. The paper gives explicit upper bounds for P(+) (sub m) = P(S sub n > or = a + b n for some n > or = m) and P(+)(sub m) = P(/S sub n/> or = a + b n for some n > or = m), a > or = 0, b > 0. These bounds immediately give the rate of convergence for the strong law of large numbers. An application is also made to a sequential selection procedure. (Author)

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1971
Accession Number
AD0735839

Entities

People

  • Rasul A. Khan

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Convergence
  • Inequalities
  • Mathematics
  • Probability
  • Random Variables

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Optical Physics and Photonics.
  • Regression Analysis.