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Original Articles

Some results on renewal equations

Pages 1159-1171 | Received 01 Aug 1987, Published online: 27 Jun 2007

References

  • Barlow , R.E. and Proschan , F. 1975 . Statistical theory of reliability and life testing, probability models , Holt, New York : Rinehart and Winston .
  • Baxter , L.A. , Scheuer , E.M. , Mcconalogue , D.J. and Blischke , W.R. 1982 . On the tabulation of the renewal function . Techno-metrics , 24 ( 2 ) : 151 – 158 .
  • Blumenthal , S. , Greenwood , J.A. and Herbach , L.H. 1976 . A comparison of the bad as old and superimposed renewal models . Management Science , 23 ( 3 ) : 280 – 286 .
  • Brown , M. 1976 . Bounds, inequalities, and monotonicity properties for some specialized renewal processes . Ann. Probability , 8 ( 2 ) : 227 – 240 .
  • Brown , M. 1976 . Further monotonicity properties for specialized renewal processes . Ann. Probability , 9 ( 5 ) : 891 – 895 .
  • Çinlar , E. 1975 . Introduction to stochastic processes , Englewood Cliffs, New Jersey : Prentice-Hall .
  • Daley , D.J. 1980 . Tight bounds for the renewal function of a random walk . Ann. Probability , 8 ( 3 ) : 615 – 621 .
  • Deligonul , Z.S. and Bilgen , S. 1984 . Solution of the Volterra equation of renewal theory with the Galerkin technique using cubic splines . J. Statist. Comput. Simul , 20 ( 3 ) : 37 – 45 .
  • Giblin , M.T. 1983 . Tables of renewal functions using a generating function algorithm , University of Bradford . Technical Report, No. UBIT 111, postgraduate School of Studies in Industrial Technology
  • Kao , E.P.C. 1983 . Computing the phase-type renewal and related functions . Technometrics , 30 ( 1 ) : 87 – 93 .
  • Marshall , A.W. and Proschan , F. . Classes Of Distributions Applicable In Replacement, with renewal theory implications . Proc. Sixth Berkeley Symp. Math. Stat. Prob . Vol. I , pp. 395 – 415 .
  • Marshall , K.T. 1973 . Linear bounds on the renewal function . SIAM J. Appl. Math , 24 ( 2 ) : 245 – 250 .
  • Smith , W.L. 1958 . Renewal theory and its ramifications . J. Roy. Statist. Soc. B , 20 ( 2 ) : 243 – 302 .
  • Soland , R.M. 1968 . Renewal functions for Gamma and Weibull distributions with increasing hazard rate , McLean, Virginia : Research Analysis Corporation . Technical Paper RAC-TP-329
  • Soland , R.M. 1969 . Availability of renewal functions for Gamma and Weibull distributions with increasing hazard rate . Operations Research , 17 : 536 – 543 .
  • Stoyan , D. and Daley , D.J. Comparison methods for queues and other stochastic models , Chichester : John Wiley & sons .
  • White , J.S. . Weibull Renewal Analysis . Proceedings of the Aerospace Reliability and Maintainability Conference . Vol. 1 , June , pp. 639 – 657 . Washington, D.C : Society of Automotive Engineers . July
  • Xie M. On the solution of renewa-type integral equations Communications in Statistics: Simulation and Computation Linköping Institute of Technology Linköping, Sweden 1986 Technical report, LiTH-IKP-R-419 To appear

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