On a Correlation Inequality and Its Applications

Abstract

This document considers a continuous distribution on (0, infinity) with cdf F, survival function F (overlined) = 1-F and cumulative hazard function H = LnF(overlined). For F NBUE it is shown that the correlation coefficient between X approx. = F and H(X) is bounded below by delta/mu, the coefficient of variation of F, while for F NWUE the correlation coefficient is bounded below by mu/delta. Several applications of this inequality and its generalizations are discussed, including Monte-Carlo simulation of the renewal function, exponential approximation of DMRL distributions, moment inequalities for record values and a variance inequality for random event epochs in a homogeneous Poisson process.

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Document Details

Document Type
Technical Report
Publication Date
Mar 29, 1988
Accession Number
ADA198295

Entities

People

  • Mark O. Brown

Organizations

  • City College of New York

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Air Force
  • Availability
  • Coefficients
  • Data Science
  • Estimators
  • Inequalities
  • Information Science
  • Intensity
  • Markov Chains
  • Mathematics
  • Monte Carlo Method
  • New York
  • Random Variables
  • Simulations
  • Stationary
  • Survival

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Statistical inference.