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Two-dimensional Renewal Function Approximation

Author

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  • Ehsan Moghimi Hadji
  • Nirmal Singh Kambo
  • Alagar Rangan

Abstract

Two-dimensional renewal functions, which are naturally extensions of one-dimensional renewal functions, have wide applicability in areas where two random variables are needed to characterize the underlying process. These functions satisfy the renewal equation, which is not amenable for analytical solutions. This paper proposes a simple approximation for the computation of the two- dimensional renewal function based only on the first two moments and the correlation coefficient of the variables. The approximation yields exact values of renewal function for bivariate exponential distribution function. Illustrations are presented to compare our approximation with that of Iskandar (1991) who provided a computational procedure which requires the use of the bivariate distribution function of the two variables. A two-dimensional warranty model is used to illustrate the approximation.

Suggested Citation

  • Ehsan Moghimi Hadji & Nirmal Singh Kambo & Alagar Rangan, 2015. "Two-dimensional Renewal Function Approximation," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(15), pages 3107-3124, August.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:15:p:3107-3124
    DOI: 10.1080/03610926.2013.815204
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    Cited by:

    1. Xiaolin Wang & Wei Xie, 2018. "Two-dimensional warranty: A literature review," Journal of Risk and Reliability, , vol. 232(3), pages 284-307, June.

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