Skip to main content
SpringerLink
Log in

Linear Estimation in Progressive Type-II Censoring

  • Chapter
  • First Online:
The Art of Progressive Censoring

Part of the book series: Statistics for Industry and Technology ((SIT))

  • 1659 Accesses

Abstract

Linear inference for progressively Type-II censored order statistics is discussed for location, scale, and location-scale families of population distributions. After a general introduction, results for exponential, generalized Pareto, extreme value, Weibull, Laplace, and logistic distributions are presented in detail.

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

References

  1. Ahsanullah M (1996) Linear prediction of generalized order statistics from two parameter exponential distributions. J Appl Stat Sci 3:1–9

    MATH  MathSciNet  Google Scholar 

  2. Ali MM, Umbach D (1998) Optimal linear inference using selected order statistics in location-scale models. In: Balakrishnan N, Rao CR (eds) Order statistics: applications. Handbook of statistics, vol 17. Elsevier, Amsterdam, pp 183–213

    Google Scholar 

  3. Arnold BC, Balakrishnan N, Nagaraja HN (1992) A first course in order statistics. Wiley, New York

    MATH  Google Scholar 

  4. Arnold BC, Balakrishnan N, Nagaraja HN (1998) Records. Wiley, New York

    Book  MATH  Google Scholar 

  5. Bain LJ, Engelhardt M (1991) Statistical analysis of reliability and life-testing models, 2nd edn. Marcel Dekker, New York

    MATH  Google Scholar 

  6. Balakrishnan N, Aggarwala R (2000) Progressive censoring: theory, methods, and applications. Birkhäuser, Boston

    Book  Google Scholar 

  7. Balakrishnan N, Cohen AC (1991) Order statistics and inference: estimation methods. Academic, Boston

    MATH  Google Scholar 

  8. Balakrishnan N, Kannan N (2001) Point and interval estimation for parameters of the logistic distribution based on progressively Type-II censored samples. In: Balakrishnan N, Rao CR (eds) Advances in reliability. Handbook of statistics, vol 20. Elsevier, Amsterdam, pp 431–456

    Google Scholar 

  9. Balakrishnan N, Rao CR (1997) Large-sample approximations to the best linear unbiased estimation and best linear unbiased prediction based on progressively censored samples and some applications. In: Panchapakesan S, Balakrishnan N (eds) Advances in statistical decision theory and applications. Birkhäuser, Boston, pp 431–444

    Chapter  Google Scholar 

  10. Balakrishnan N, Saleh HM (2011) Relations for moments of progressively Type-II censored order statistics from half-logistic distribution with applications to inference. Comput Stat Data Anal 55:2775–2792

    Article  MATH  MathSciNet  Google Scholar 

  11. Balakrishnan N, Saleh HM (2012) Relations for moments of progressively Type-II censored order statistics from log-logistic distribution with applications to inference. Comm Stat Theory Meth 41:880–906

    Article  MATH  Google Scholar 

  12. Balakrishnan N, Saleh HM (2013) Recurrence relations for single and product moments of progressively Type-II censored order statistics from a generalized half-logistic distribution with application to inference. J Stat Comput Simul 83:1704–1721

    Article  MathSciNet  Google Scholar 

  13. Balakrishnan N, Sandhu RA (1996) Best linear unbiased and maximum likelihood estimation for exponential distributions under general progressive Type-II censored samples. Sankhyā Ser B 58:1–9

    MATH  MathSciNet  Google Scholar 

  14. Balakrishnan N, Chandramouleeswaran M, Ambagaspitiya R (1996) BLUEs of location and scale parameters of Laplace distribution based on type-II censored samples and associated inference. Microelectron Reliab 36:371–374

    Article  Google Scholar 

  15. Balakrishnan N, Cramer E, Kamps U, Schenk N (2001b) Progressive type II censored order statistics from exponential distributions. Statistics 35:537–556

    Article  MATH  MathSciNet  Google Scholar 

  16. Balakrishnan N, Burkschat M, Cramer E (2008a) Best linear equivariant estimation and prediction in location-scale families. Sankhyā Ser B 70:229–247

    MATH  MathSciNet  Google Scholar 

  17. Balakrishnan N, AL-Hussaini EK, Saleh HM (2011a) Recurrence relations for moments of progressively censored order statistics from logistic distribution with applications to inference. J Stat Plan Infer 141:17–30

    Google Scholar 

  18. Balasooriya U, Balakrishnan N (2000) Reliability sampling plans for the lognormal distribution, based on progressively censored samples. IEEE Trans Reliab 49:199–203

    Article  Google Scholar 

  19. Bondesson L (1979) On best equivariant and best unbiased equivariant estimators in the extended Gauss-Markov model. Scand J Stat 6:22–28

    MATH  MathSciNet  Google Scholar 

  20. Burkschat M (2010) Linear estimators and predictors based on generalized order statistics from generalized Pareto distributions. Comm Stat Theory Meth 39:311–326

    Article  MATH  MathSciNet  Google Scholar 

  21. Burkschat M, Cramer E, Kamps U (2006) On optimal schemes in progressive censoring. Stat Probab Lett 76:1032–1036

    Article  MATH  MathSciNet  Google Scholar 

  22. Burkschat M, Cramer E, Kamps U (2007a) Linear estimation of location and scale parameters based on generalized order statistics from generalized Pareto distributions. In: Ahsanullah M, Raqab M (eds) Recent developments in ordered random variables. Nova Science Publisher, New York, pp 253–261

    Google Scholar 

  23. Christensen R (2011) Plane answers to complex questions: the theory of linear models, 4th edn. Springer, New York

    Book  Google Scholar 

  24. Cramer E, Kamps U (1998) Sequential k-out-of-n systems with Weibull components. Econ Qual Control 13:227–239

    MATH  Google Scholar 

  25. David HA, Nagaraja HN (2003) Order statistics, 3rd edn. Wiley, Hoboken

    Book  MATH  Google Scholar 

  26. Govindarajulu Z (1966) Best linear estimates under symmetric censoring of the parameters of double exponential population. J Am Stat Assoc 61:248–258

    MathSciNet  Google Scholar 

  27. Hofmann G, Cramer E, Balakrishnan N, Kunert G (2005a) An asymptotic approach to progressive censoring. J Stat Plan Infer 130:207–227

    Article  MATH  MathSciNet  Google Scholar 

  28. Johnson NL, Kotz S, Balakrishnan N (1994) Continuous univariate distributions, vol 1, 2nd edn. Wiley, New York

    Google Scholar 

  29. Kotz S, Kozubowski TJ, Podgórski K (2001) The Laplace distribution and generalizations. A revisit with applications to communications, economics, engineering, and finance. Birkhäuser, Boston

    Google Scholar 

  30. Kulldorff G, Vännman K (1973) Estimation of the location and scale parameters of a Pareto distribution by linear functions of order statistics. J Am Stat Assoc 68:218–227

    Article  MATH  Google Scholar 

  31. Lieblein J (1953) On the exact evaluation of the variances and covariances of order statistics in samples from the extreme-value distribution. Ann Math Stat 24:282–287

    Article  MATH  MathSciNet  Google Scholar 

  32. Lieblein J (1955) On moments of order statistics from the Weibull distribution. Ann Math Stat 26:330–333

    Article  MATH  MathSciNet  Google Scholar 

  33. Madi MT, Raqab MZ (2007) Bayesian prediction of rainfall records using the generalized exponential distribution. Environmetrics 18:541–549

    Article  MathSciNet  Google Scholar 

  34. Mann NR (1969b) Optimum estimators for linear functions of location and scale parameters. Ann Math Stat 40:2149–2155

    Article  MATH  Google Scholar 

  35. Mann NR (1971) Best linear invariant estimation for Weibull parameters under progressive censoring. Technometrics 13:521–533

    Article  MATH  MathSciNet  Google Scholar 

  36. Nelson W (1982) Applied life data analysis. Wiley, New York

    Book  MATH  Google Scholar 

  37. Ogawa J (1951) Contributions to the theory of systematic statistics. I. Osaka Math J 3: 175–213

    MathSciNet  Google Scholar 

  38. Pickands J (1975) Statistical inference using extreme order statistics. Ann Stat 3:119–131

    Article  MATH  MathSciNet  Google Scholar 

  39. Raqab MZ, Asgharzadeh A, Valiollahi R (2010) Prediction for Pareto distribution based on progressively Type-II censored samples. Comput Stat Data Anal 54:1732–1743

    Article  MATH  MathSciNet  Google Scholar 

  40. Reiss RD (1989) Approximate distributions of order statistics. Springer, New York

    Book  MATH  Google Scholar 

  41. Sarhan AE (1954) Estimation of the mean and standard deviation by order statistics. Ann Math Stat 25:317–328

    Article  MATH  MathSciNet  Google Scholar 

  42. Sarhan AE (1955) Estimation of the mean and standard deviation by order statistics, part III. Ann Math Stat 26:576–592

    Article  MathSciNet  Google Scholar 

  43. Sarhan AE, Greenberg BG (1959) Estimation of location and scale parameters for the rectangular population from censored samples. J Roy Stat Soc Ser B 21:356–363

    MATH  Google Scholar 

  44. Takada Y (1982) A comment on best invariant predictors. Ann Stat 10:971–978

    Article  MATH  MathSciNet  Google Scholar 

  45. Thomas DR, Wilson WM (1972) Linear order statistic estimation for the two-parameter Weibull and extreme value distribution from Type-II progressively censored samples. Technometrics 14:679–691

    Article  MATH  Google Scholar 

  46. Vännman K (1976) Estimators based on order statistics from a Pareto distribution. J Am Stat Assoc 71:704–708

    MATH  Google Scholar 

  47. Viveros R, Balakrishnan N (1994) Interval estimation of parameters of life from progressively censored data. Technometrics 36:84–91

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada

    N. Balakrishnan

  2. Institute of Statistics, RWTH Aachen University, Aachen, Germany

    Erhard Cramer

Authors
  1. N. Balakrishnan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Erhard Cramer
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media New York

About this chapter

Cite this chapter

Balakrishnan, N., Cramer, E. (2014). Linear Estimation in Progressive Type-II Censoring. In: The Art of Progressive Censoring. Statistics for Industry and Technology. Birkhäuser, New York, NY. https://doi.org/10.1007/978-0-8176-4807-7_11

Download citation

Publish with us

Policies and ethics

Search

Navigation