Skip to main content

A chi-square goodness-of-fit test for exponential distributions of the first order

Part of the Lecture Notes in Mathematics book series (LNM,volume 1412)

Keywords

  • Minimum Variance Unbiased Estimator
  • Additive Number Theory
  • Estimate Distribution Function
  • Power Series Distribution
  • Truncate Power Series

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bol'shev L.N. Cluster analysis.-Bull.Int.Stat.Inst., 1969, 43, 411–425.

    MathSciNet  MATH  Google Scholar 

  2. Bol'shev L.N., Mirvaliev M. Chi-square goodness-of.fit test for the Poisson, binomial and negative binomial distributions.-Teor Veroyatn. Primen. 1978, 23, 461–474.

    MathSciNet  MATH  Google Scholar 

  3. Chernoff H., Lehmann L. The use of maximum likelihood estimates in tests for goodness of fit.-Ann.Math.Stat., 1954, 25, 579–586.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Chibisov D.M. Certain chi-square type tests for continuous distributions.-Teor.Veroyatn.Primen., 1971, 16, 3–20.

    MATH  Google Scholar 

  5. Drost F.G. Asymptotics for generalized chi-square goodness-of-fit test.-Vrije Univ., de Boelelaan, Amsterdam, 1987.

    MATH  Google Scholar 

  6. Dzhaparidze K.O., Nikulin M.S. Probability distributions of the Kolmogorov and omega-square statistics for continuous distributions with shift and scale parameters.-Zap.Nauchn.Semin.Leningr.Otd.Mat. Inst. Steklova, 1978, 85, 46–74.

    MathSciNet  MATH  Google Scholar 

  7. Greenwood P.E., Nikulin M.S. Some remarks on the application of chisquare type tests.-Zap.Nauchn.Semin.Leningr.Otd.Mat.Inst.Steklova, 1987, 153, 49–71.

    MATH  Google Scholar 

  8. Gupta R.C. Minimum variance unbased estimation in a modified power series distribution and some of its applications.-Commun.Statist. Theor.Meth., 1977, 6, 977–991.

    CrossRef  MATH  Google Scholar 

  9. Joshi S.W., Park C.J. Minimum variance unbased estimation for truncated power series distribution.-Sankhyá: 1974, A36, 305–314.

    MathSciNet  MATH  Google Scholar 

  10. Kallenberg W.C.M., Oosterhoff J., Schriever B.F. The number of classes in chi-squared goodness-of-fit tests.-JASA, 1985, 80, 959–968.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Karakostas R.X. On minimum variance unbased estimators.-Am.Stat. 1985, 39, 303–305.

    MathSciNet  Google Scholar 

  12. McCulloch C.E. Relationsships among some chi-square goodness-of-fit statistics.-Commun.Stat. Theor.Meth., 1985, 14,593–603.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. Moore D. A chi-square statistic with random cell boundaries.-Ann. Math.Stat., 1971, 42, 147–156.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. Nikulin M.S. Chi-square test for continuous distributions with shift and scale parameters.-Teor.Veroyatn.Primen., 1973, 18, 559–568.

    MathSciNet  MATH  Google Scholar 

  15. Nikulin M.S. On the chi-square test for continuous distributions.-Teor.Veroyatn.Primen., 1973, 18, 675–679.

    MathSciNet  Google Scholar 

  16. Noack A. A class of random variables with discrete distributions.-Ann.Math.Stat., 1950, 21, 127–132.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. Oosterhoff J. The choice of cells in chi-square tests.-Statist. Neerl., 1985, 39, 115–128.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. Park C.J. The distribution of requency of the geometrical distribution.-Sankhyá: 1973, A35, 106–111.

    Google Scholar 

  19. Patil G.P. Minimum variance unbased estimation and certain problems of additive number theory.-Ann.Math.Stat., 1963, 34, 1050–1056.

    CrossRef  MATH  Google Scholar 

  20. Pollard D. General chi-square goodness-of-fit tests with data-dependent cells.-Z.Wahrscheinlichkeitstheor. Verw.Geb., 1979, 50, 317–331.

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. Rao K., Robson D.S. A chi-squared statistic for goodness-of-fit tests within the exponential family.-Commun.Stat., 1973, 3, 1139–1153.

    MathSciNet  MATH  Google Scholar 

  22. Watson G.S. On chi-square goodness-of-fit tests for continuous distributions.-J.R.Stat.Soc., 1958, B20, 44–61.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1989 Springer-Verlag

About this chapter

Cite this chapter

Nikulin, M.S., Voinov, V.G. (1989). A chi-square goodness-of-fit test for exponential distributions of the first order. In: Kalashnikov, V.V., Zolotarev, V.M. (eds) Stability Problems for Stochastic Models. Lecture Notes in Mathematics, vol 1412. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084176

Download citation

  • DOI: https://doi.org/10.1007/BFb0084176

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51948-5

  • Online ISBN: 978-3-540-46863-9

  • eBook Packages: Springer Book Archive