Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-23T05:47:37.188Z Has data issue: false hasContentIssue false
  • English
  • Français

On excess life in certain renewal processes

Published online by Cambridge University Press:  14 July 2016

Barry C. Arnold  and
Richard A. Groeneveld
Barry C. Arnold*
Affiliation:
University of California, Riverside
Richard A. Groeneveld*
Affiliation:
Iowa State University
*
∗Postal address: Department of Statistics, University of California, Riverside, CA 92521, U.S.A.
∗∗Postal address: Department of Statistics, Iowa State University, Snedecor Hall, Ames, IA 50011, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

Excess life distributions for discrete renewal processes may be computed by using elementary discrete Markov chain concepts involving absorption probabilities. Excess life distributions in general may then be obtained by approximating the renewal process under study by a suitably chosen sequence of discrete renewal processes. The technique is illustrated in the cases of renewal processes with interarrival distributions which are a linear combination of two exponentials and uniform [0, 1]. A related algorithm is described for computer generated approximations of excess life distributions corresponding to continuous interarrival time distributions with an increasing c.d.f. Conditions for convergence of this algorithm are examined.

Keywords

ALGORITHM FOR EXCESS LIFE APPROXIMATIONDISCRETE RENEWAL PROCESSESEXCESS LIFE DISTRIBUTIONSMARKOV CHAINS IN RENEWAL PROCESSESRENEWAL EQUATIONUNIFORM RENEWAL PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 2 , June 1981 , pp. 378 - 389
Copyright
Copyright © Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Feller, W. (1966) An Introduction to Probability Theory and its Applications, Vol. II. Wiley, New York.Google Scholar
Kemeny, J. G. and Snell, J. L. (1960) Finite Markov Chains. Van Nostrand, Princeton, N.J.Google Scholar
Parzen, E. (1962) Stochastic Processes. Holden-Day, San Francisco.Google Scholar
Skellam, J. G. and Shenton, L. R. (1957) Distributions associated with random walk and recurrent events (with discussion). J. R. Statist. Soc. B 19, 64–118.Google Scholar
Smith, W. L. (1958) Renewal theory and its ramifications (with discussion). J.R. Statist. Soc. B 20, 243–302.Google Scholar