Statistical analysis of reliability data in renewal processes

  • Shun-ichi Abe


Renewal Process Observation Interval Lifetime Distribution Nonparametric Estimator Renewal Theory 


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  1. [1]
    Abe, S. (1970). Asymptotic behavior of some nonparametric statistics in an extended failure model—1 and 2,Rep. Stat. Appl. Res., JUSE,17, 163–186.MATHGoogle Scholar
  2. [2]
    Abe, S. (1971). Nonparametric estimates of transition distributions in Markov renewal processes, to appear inRep. Stat. Appl. Res., JUSE.Google Scholar
  3. [3]
    Cox, D. R. (1962).Renewal, Theory, London: Methuen.MATHGoogle Scholar
  4. [4]
    Cox, D. R. and Lewis, P. A. W. (1966).The Statistical Analysis of Series of Events, London: Methuen.MATHGoogle Scholar
  5. [5]
    Doob, J. L. (1953).Stochastic Processes, Wiley.Google Scholar
  6. [6]
    Feller, W. (1950, 1966).An Introduction to Probability Theory and Its Applications Volumes I and II, Wiley.Google Scholar
  7. [7]
    Gnedenko, B. V. and Kolmogorov, A. N. (1954).Limit Distributions for Sums of Independent Random Variables, Addison-Wesley.Google Scholar
  8. [8]
    Lotka, A. J. (1939). A contribution to the theory of self-renewing aggregates, with special reference to industrial replacement,Ann. Math. Statist.,10, 1–25.MATHGoogle Scholar

Copyright information

© Institute of Statistical Mathematics 1971

Authors and Affiliations

  • Shun-ichi Abe
    • 1
  1. 1.Railway Technical Research InstituteJapanese National RailwaysJapan

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