Some new bounds for the mean value function of the residual lifetime process

PEKALP M. H.

STATISTICS & PROBABILITY LETTERS, vol.187, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 187
  • Publication Date: 2022
  • Doi Number: 10.1016/j.spl.2022.109497
  • Journal Name: STATISTICS & PROBABILITY LETTERS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, DIALNET
  • Keywords: Renewal process, Mean residual lifetime function, Integral equation, MONOTONICITY PROPERTIES, RENEWAL, RUIN
  • Ankara University Affiliated: Yes

Abstract

In this study, mean residual lifetime (MRL) function of the residual lifetime process is investigated. Various two-sided bounds are obtained for this function by using the monotone convergence of the sequence of the functions. Since many important features of any stochastic process depend on classifications of distributions, improved bounds are found for MRL function by considering the taxonomy of the distributions. Moreover, some new bounds are achieved by using the asymptotic expression of MRL function and its boundary relation with the MRL of a single component at age t. Three examples are given to illustrate the results proposed.(C) 2022 Elsevier B.V. All rights reserved.