Skip to main content
SpringerLink
Log in

Decreasing Percentile Residual Life: Properties and Estimation

  • Chapter
  • First Online:
Stochastic Orders in Reliability and Risk

Part of the book series: Lecture Notes in Statistics ((LNSP,volume 208))

  • 2073 Accesses

Abstract

In this work we describe the class of distribution functions with decreasing α-percentile residual life [DPRL(α)], 0 < α < 1. The close relationship between the aging notion DPRL(α) and increasing failure rate (IFR) will be discussed, as well as the relationship between the DPRL(α) and the percentile residual life orders. Besides, we introduce an estimator of the percentile residual life function, under the condition that it decreases, in the censored and the non-censored case. Finally, a real data illustration is provided.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Bibliography

  1. Aly, E.-E.A.A.: On some confidence bands for percentile residual life functions. Journal of Nonparametric Statistics, 2, 59–70 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  2. Barabás, B., Csörgö, M., Horváth, L. and Yandell, B. S.: Bootstrapped confidence bands for percentile lifetime. Annals of the Institute of Statistical Mathematics, 38, 429–438 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  3. Belzunce, F., Gao, X., Hu, T. and Pellerey, F.: Characterizations of the hazard rate order and IFR aging notion. Statistics and Probability Letters, 70, 235–242 (2004)

    Article  MathSciNet  Google Scholar 

  4. Borgan, Ø.: Nelson-Aalen estimator. Online Encyclopedia of Biostatistics, John Wiley & Sons, Ltd (2005)

    Google Scholar 

  5. Bryson, M. C. and Siddiqui, M. M.: Some criteria for aging. Journal of the American Statistical Association, 64, 1472–1483 (1969)

    Article  MathSciNet  Google Scholar 

  6. Chung, C. F.: Confidence bands for percentile residual lifetime under random censorship model. Journal of Multivariate Analysis, 29, 94–126 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  7. Csörgö, M. and Csörgö, S.: Estimation of percentile residual life. Operations Research, 35, 598–606 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  8. Csörgö, S. and Mason, D. M.: Bootstrapping empirical functions. Annals of Statistics, 17, 1447–1471 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  9. Csörgö, S. and Viharos, L.: Confidence bands for percentile residual lifetimes. Journal of Statistical Planning and Inference, 30, 327–337 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  10. Franco-Pereira, A. M. and de Uña-Álvarez, J.: Estimation of a monotone percentile residual life function under random censorship. Technical Report, Department of Statistics and OR, University of Vigo (2012)

    Google Scholar 

  11. Franco-Pereira, A. M., Lillo, R. E. and Romo, J.: Characterization of bathtub distributions via percentile residual life functions. UC3M Working papers. Statistics and Econometrics, 10–12 (2010)

    Google Scholar 

  12. Franco-Pereira, A. M., Lillo, R. E., Romo, J. and Shaked, M.: The percentile residual life orders. Applied Stochastic Models in Business and Industry, 27, 235–252 (2010)

    Article  MathSciNet  Google Scholar 

  13. Franco-Pereira, A. M., Lillo, R. E. and Shaked, M.: The decreasing percentile residual life aging notion. Statistics, to appear (2011)

    Google Scholar 

  14. Haines, A. L. and Singpurwalla, N. D.: Some contributions to the stochastic characterization of wear. Reliability and Biometry, Statistical Analysis of Lifelength (edited by F. Proschan and R.J. Serfling), SIAM, Philadelphia, 47–80 (1974)

    Google Scholar 

  15. Joe, H. and Proschan, F.: Percentile residual life functions. Operations Research, 32, 668–678 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  16. Joe, H. and Proschan, F.: Comparison of two life distributions on the basis of their percentile residual life functions. The Canadian Journal of Statistics, 12, 91–97 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  17. Launer, R. L.: Graphical techniques for analyzing failure data with the percentile residual-life function. IEEE Transactions on Reliability, 42, 71–75, 80 (1993)

    Google Scholar 

  18. Muth, E. J.: Reliability models with positive memory derived from the mean residual life function. Theory and Applications of Reliability (edited by C.P. Tsokos and I.N. Shimi), Academic Press, New York (1977)

    Google Scholar 

  19. Shaked, M. and Shanthikumar, J. G.: Stochastic Orders. Springer, New York (2007)

    Book  MATH  Google Scholar 

  20. Watson, G. S. and Wells, W. T.: On the possibility of improving the mean useful life of items by eliminating those with short lives. Technometrics, 3, 281–298 (1961)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. SiDOR Research Group, Universidad de Vigo, Vigo (Pontevedra), Spain

    Alba M. Franco-Pereira

  2. Department of Statistics and Operations Research, Universidad de Vigo, Vigoc (Pontevedra), Spain

    Jacobo de Uña

  3. Department of Statistics, Universidad Carlos III de Madrid, Getafe (Madrid), Spain

    Rosa E. Lillo

  4. Department of Mathematics, University of Arizona, Tuscon, AZ, 85721, USA

    Moshe Shaked

Authors
  1. Alba M. Franco-Pereira
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jacobo de Uña
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rosa E. Lillo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Moshe Shaked
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alba M. Franco-Pereira .

Editor information

Editors and Affiliations

  1. Dept. Mathematics, Washington State University, Lighty 370, Pullman, 99164, Washington, USA

    Haijun Li

  2. Xiamen University, Xiamen, 361000, China, People's Republic

    Xiaohu Li

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this chapter

Cite this chapter

Franco-Pereira, A.M., de Uña, J., Lillo, R.E., Shaked, M. (2013). Decreasing Percentile Residual Life: Properties and Estimation. In: Li, H., Li, X. (eds) Stochastic Orders in Reliability and Risk. Lecture Notes in Statistics(), vol 208. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6892-9_9

Download citation

Publish with us

Policies and ethics

Search

Navigation