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Year 2019, , 54 - 57, 27.12.2019
https://doi.org/10.17678/beuscitech.556451

Abstract

References

  • [1] Ross, M.S., 1983. Stochastic Processes. John Wiley&Sons, 510, New York.
  • [2] Karlın, S., and Taylor H. M., 1975. A First Course in Stochastic Processes, Second edition. Acedemic Press, 557, New York, 1975.
  • [3] Tijms, 1994. Stochastic Models: An Algorithmic Approach, John Wiley&Sons, New York, 1994.
  • [4] Tamam D., 2008. Tam ve Sansürlü Örneklem Durumlarında Weibull Dağılımı için Bazı İstatistiki Sonuç Çıkarımları, Yüksek Lisans Tezi. Ankara Üniversitesi, Ankara.
  • [5] Lawless, J. F., 2003. Statistical Models and Methods for Lifetime Data, John Wiley&Sons, 630, Canada.
  • [6] Schneider H., Lın B. S., and O’cınneide C., 1990. Comparison of Nonparemetrik Estimators for the Renewal Function. Journal Roy. Statist. Soc. Ser. C., 39, 55-61.

Nonparametric estimation of a renewal function in the case of censored sample

Year 2019, , 54 - 57, 27.12.2019
https://doi.org/10.17678/beuscitech.556451

Abstract



A renewal process is a counting process which counts the number of renewals that occurs as a function of time, wherein the durations between successive renewals are random variables independent of one another, with identical F distributions. The mean value function data is frequently needed in applications of renewal processes. For the renewal function, open expressions depending on distribution function F can be calculated from each other. However, even though the distribution function F is known, the renewal function cannot be obtained analytically except for a few distributions. In this study, in the case that F is totally unknown, life table management and Kaplan-Meier estimator were used depending on random right-censored sampling for the estimation of F value. Then, for the estimation of the renewal function value in the random right-censored data, nonparametric estimators were proposed and the problem of how to calculate these estimators were discussed.

References

  • [1] Ross, M.S., 1983. Stochastic Processes. John Wiley&Sons, 510, New York.
  • [2] Karlın, S., and Taylor H. M., 1975. A First Course in Stochastic Processes, Second edition. Acedemic Press, 557, New York, 1975.
  • [3] Tijms, 1994. Stochastic Models: An Algorithmic Approach, John Wiley&Sons, New York, 1994.
  • [4] Tamam D., 2008. Tam ve Sansürlü Örneklem Durumlarında Weibull Dağılımı için Bazı İstatistiki Sonuç Çıkarımları, Yüksek Lisans Tezi. Ankara Üniversitesi, Ankara.
  • [5] Lawless, J. F., 2003. Statistical Models and Methods for Lifetime Data, John Wiley&Sons, 630, Canada.
  • [6] Schneider H., Lın B. S., and O’cınneide C., 1990. Comparison of Nonparemetrik Estimators for the Renewal Function. Journal Roy. Statist. Soc. Ser. C., 39, 55-61.
There are 6 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Çiğdem Cengiz

Publication Date December 27, 2019
Submission Date April 20, 2019
Published in Issue Year 2019

Cite

IEEE Ç. Cengiz, “Nonparametric estimation of a renewal function in the case of censored sample”, Bitlis Eren University Journal of Science and Technology, vol. 9, no. 2, pp. 54–57, 2019, doi: 10.17678/beuscitech.556451.