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Bayesian estimation of the expected time of first arrival past a truncated time T: the case of NHPP with power law intensity

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Abstract

Non-homogenous Poisson process, \(\{N(t), t > 0\}\) under time-truncated sampling scheme is often used in practice. \(E[S_{N(T)+1}\)], the expected time of arrival of the first event after a truncated time \(T\), is expressed as a function of intensity. A non-informative prior as well as gamma priors for Power Law intensity function are used to obtain Bayes estimates of the expected time.

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References

  • Ascher H, Feingold H (1984) Repairable systems reliability. Dekker, New York

    MATH  Google Scholar 

  • Calabria R, Guida M, Pulcini G (1992) A Bayes procedure for estimation of current system reliability. IEEE Transon Reliabi 41(4):69–92

    Google Scholar 

  • Cox DR, Lewis PAW (1966) The statistical analysis of series of events. Methuen, London

    Book  MATH  Google Scholar 

  • Crow LH (1982) Confidence interval procedures for the Weibull process with applications to reliability growth. Technometrics 24:67–72

    Article  MathSciNet  MATH  Google Scholar 

  • Guida M, Calabria R, Pulcini G (1989) Bayes inference for a nonhomogenous Poisson processes with power law intensity law. IEEE Trans Reliabi 38(5):603–609

    Article  MATH  Google Scholar 

  • Kyparisis J, Singpurwalla ND (1985) Bayesian inference for Weibull process with applications to assessing software reliability growth and predicting software failures. In: Computer science and statistics: proceedings of the 16th symposium on the interface, pp 57–64

  • Park WJ, Kim YG (1992) Goodness-of-fit tests for the power-law process. IEEE Trans Reliab 41(1):107–111

    Article  MATH  Google Scholar 

  • Pasupathy R (2010) Generating nonhomogeneous Poisson processes. In: Wiley encyclopedia of operations research and management science. Wiley, pp 1–11 (2010)

  • Proschan F (1963) Theoretical explanation of observed decreasing failure rate. Technometrics 5(3):375–383

    Article  Google Scholar 

  • Ross SM (2009) Introduction to probability models, 10th edn. Academic Press, San Diego

    Google Scholar 

  • Shaul KBL, Idit L, Benjamin R (1992) Bayesian inference for the power law process. Ann Inst Stat Math 44(4):623–639

    Article  MATH  Google Scholar 

  • Taghipour S, Banjevic D (2011) Trend analysis of the power law process with censored data. In: Reliability and maintainability symposium proceedings-annual, pp 1–6

  • Wang YP, Lu ZZ (2011) Bayesian inference and prediction analysis of the power law process based on a gamma prior distribution. Commun Stat Simul Comput 40:1383–1401

    Article  MATH  Google Scholar 

  • Yan ZQ, Li XX, Xie HW, Jiang YJ (2008) Bayesian synthetic evaluation of multistage reliability growth with instant and delayed fix modes. J Syst Eng Electron 19(6):1294–1301

    Article  Google Scholar 

  • Yin L, Trivedi KS (1999) Confidence interval estimation of NHPP-based software reliability models. In: 10th International symposium on software reliability engineering, pp 1–7

Download references

Acknowledgments

The author is very grateful to the co-editor, the associate editor, and the reviewers for their constructive comments that greatly improved the presentation of the results.

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  1. Department of Mathematics, Towson University, Towson, MD, 21252, USA

    M. S. Aminzadeh

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  1. M. S. Aminzadeh
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Correspondence to M. S. Aminzadeh.

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Aminzadeh, M.S. Bayesian estimation of the expected time of first arrival past a truncated time T: the case of NHPP with power law intensity. Comput Stat 28, 2465–2477 (2013). https://doi.org/10.1007/s00180-013-0414-9

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  • DOI: https://doi.org/10.1007/s00180-013-0414-9

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