Skip to main content

Goodness-of-Fit Tests in Progressive Type-II Censoring

  • Chapter
  • First Online:
Book cover The Art of Progressive Censoring

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

  • 1673 Accesses

Abstract

Goodness-of-fit tests for progressively Type-II censored data are reviewed. The presentation includes tests on exponentiality as well as tests for other distributional assumptions.

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

Access this chapter

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. Balakrishnan N, Lin CT (2003) On the distribution of a test for exponentiality based on progressively type-II right censored spacings. J Stat Comput Simul 73:277–283

    Article  MATH  MathSciNet  Google Scholar 

  2. 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 

  3. Balakrishnan N, Ng HKT, Kannan N (2002c) A test of exponentiality based on spacings for progressively type-II censored data. In: Huber-Carol C, Balakrishnan N, Nikulin M, Mesbah M (eds) Goodness-of-fit tests and model validity. Birkhäuser, Boston, pp 89–111

    Chapter  Google Scholar 

  4. Balakrishnan N, Ng HKT, Kannan N (2004b) Goodness-of-fit tests based on spacings for progressively type-II censored data from a general location-scale distribution. IEEE Trans Reliab 53:349–356

    Article  Google Scholar 

  5. Balakrishnan N, Habibi Rad A, Arghami NR (2007) Testing exponentiality based on Kullback-Leibler information with progressively Type-II censored data. IEEE Trans Reliab 56:301–307

    Article  Google Scholar 

  6. Bradley DM, Gupta RC (2002) On the distribution of the sum of n non-identically distributed uniform random variables. Ann Inst Stat Math 54:689–700

    Article  MATH  MathSciNet  Google Scholar 

  7. Brockwell PJ, Davis RA (2009) Time series: theory and methods, 2nd edn. Springer, New York

    Google Scholar 

  8. Brunk HD (1962) On the range of the difference between hypothetical distribution function and Pyke’s modified empirical distribution function. Ann Math Stat 33:525–532

    Article  MATH  MathSciNet  Google Scholar 

  9. Buckle N, Kraft C, Eeden Cv (1969) An approximation to the Wilcoxon-Mann-Whitney distribution. J Am Stat Assoc 64:591–599

    Article  MATH  Google Scholar 

  10. Chen G, Balakrishnan N (1995) A general purpose approximate goodness-of-fit test. J Qual Tech 27:154–161

    Google Scholar 

  11. D’Agostino RB, Stephens MA (eds) (1986) Goodness-of-fit techniques. Marcel Dekker, New York

    MATH  Google Scholar 

  12. Durbin J (1969) Tests for serial correlation in regression analysis based on the periodogram of least-squares residuals. Biometrika 56:1–15

    Article  MATH  MathSciNet  Google Scholar 

  13. Feller W (1971) An introduction to probability theory and its applications, vol II, 2nd edn. Wiley, New York

    MATH  Google Scholar 

  14. Fischer T, Kamps U (2011) On the existence of transformations preserving the structure of order statistics in lower dimensions. J Stat Plan Infer 141:536–548

    Article  MATH  MathSciNet  Google Scholar 

  15. Greenwood M (1946) The statistical study of infectious diseases. J Roy Stat Soc 109: 85–110

    Article  MathSciNet  Google Scholar 

  16. Hegazy YAS, Green JR (1975) Some new goodness-of-fit tests using order statistics. Appl Stat 24:299–308

    Article  Google Scholar 

  17. Huffer FW, Lin CT (2001) Computing the joint distribution of general linear combinations of spacings or exponential variates. Stat Sinica 11:1141–1157

    MATH  MathSciNet  Google Scholar 

  18. Kendall MG, Stuart A, Ord JK (1987) Kendall’s advanced theory of statistics, vol I, 5th edn. Griffin, London

    MATH  Google Scholar 

  19. King JR (1971) Probability charts for decision making. Industrial Press, New York

    Google Scholar 

  20. Lin CT, Huang YL, Balakrishnan N (2008) A new method for goodness-of-fit testing based on Type-II right censored samples. IEEE Trans Reliab 57:633–642

    Article  Google Scholar 

  21. Marohn F (2002) A characterization of generalized Pareto distributions by progressive censoring schemes and goodness-of-fit tests. Comm Stat Theory Meth 31:1055–1065

    Article  MATH  MathSciNet  Google Scholar 

  22. Michael JR, Schucany WR (1979) A new approach to testing goodness of fit for censored samples. Technometrics 21:435–441

    Article  MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

  24. Pakyari R, Balakrishnan N (2012) A general purpose approximate goodness-of-fit test for progressively Type-II censored data. IEEE Trans Reliab 61:238–244

    Article  Google Scholar 

  25. Pakyari R, Balakrishnan N (2013) Goodness-of-fit tests for progressively Type-II censored data from location-scale distributions. J Stat Comput Simul 83:167–178

    Article  MATH  MathSciNet  Google Scholar 

  26. Park S (2005) Testing exponentiality based on Kullback-Leibler information with the Type-II censored data. IEEE Trans Reliab 54:22–26

    Article  Google Scholar 

  27. Quesenberry C, Miller F (1977) Power studies of some tests for uniformity. J Stat Comput Simul 5:169–191

    Article  MATH  Google Scholar 

  28. Rad AH, Yousefzadeh F, Balakrishnan N (2011) Goodness-of-fit test based on Kullback-Leibler information for progressively Type-II censored data. IEEE Trans Reliab 60:570–579

    Article  Google Scholar 

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

    Book  MATH  Google Scholar 

  30. Sanjel D, Balakrishnan N (2008) A Laguerre polynomial approximation for a goodness-of-fit test for exponential distribution based on progressively censored data. J Stat Comput Simul 78:503–513

    Article  MATH  MathSciNet  Google Scholar 

  31. Schoenberg IJ (1946) Contributions to the problem of approximation of eqidistant data by analytic functions, part A: on the problem of smoothing or graduation, a first class of analytic approximation formulas. Quart Appl Math 4:45–99

    MathSciNet  Google Scholar 

  32. Shapiro SS, Wilk MB (1972) An analysis of variance test for the exponential distribution (complete samples). Technometrics 14:355–370

    Article  MATH  Google Scholar 

  33. Spinelli JJ, Stephens MA (1987) Tests for exponentiality when origin and scale parameters are unknown. Technometrics 29:471–476

    Article  MathSciNet  Google Scholar 

  34. Stephens MA (1969) Results from the relation between two statistics of the Kolmogorov-Smirnov type. Ann Math Stat 40:1833–1837

    Article  MATH  MathSciNet  Google Scholar 

  35. Tiku M (1980) Goodness of fit statistics based on the spacings of complete or censored samples. Aust J Stat 22:260–275

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  37. Wang BX (2008) Goodness-of-fit test for the exponential distribution based on progressively Type-II censored sample. J Stat Comput Simul 78:125–132

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

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). Goodness-of-Fit Tests 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_19

Download citation

Publish with us

Policies and ethics