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Sankhya B

, Volume 73, Issue 1, pp 1–19 | Cite as

On the distribution of burr with applications

  • Ratan DasguptaEmail author
Article

Abstract

Under certain conditions, the distribution of burr is shown to follow an extreme value distribution. In this context, a result on extremal process based on stationary sequence is proved. Some data sets are analyzed and applications of the results indicated.

Keywords

Burr Ornstein-Uhlenbeck process Confidence ellipse Preferred direction 

Mathematics Subject Classifications (2010)

Primary 62E20; Secondary 62-07 60G70 60F99 

Notes

Acknowledgements

Thanks are due to Professor J.K.Ghosh for interesting discussions, Professor Debasis Sengupta for help in computer programming, Mr. N.T.V.Ranga Rao for suggesting the problem and Mr. E. M. Vyasa for providing data. Referee’s suggestions improved the presentation.

References

  1. Dasgupta, R. 2006. Modeling of material Wastage by Ornstein—Uhlenbeck process. Calcutta Statistical Association Bulletin 58:15–35.MathSciNetzbMATHGoogle Scholar
  2. Dasgupta, R., J.K. Ghosh, and N.T.V. Ranga Rao. 1981. A cutting model and distribution of ovality and related topics. In Proc. of the ISI golden jubilee conference, 182–204.Google Scholar
  3. Galambos, J. 1987. The asymptotic theory and extreme order statistics 2nd edn. Krieger.Google Scholar
  4. Hu̇sler, J., and L. Peng. 2008. Review of testing issues in extremes: In honor of Professor Laurens de Haan. Extremes 11:99–111. doi: 10.1007/s10687-007-0052-0.MathSciNetCrossRefGoogle Scholar
  5. Johnson, N., S. Kotz, and N. Balakrishnan. 1995. Continuous univariate distributions vol. 2. New York: Wiley.zbMATHGoogle Scholar
  6. Karlin, S., and H.M. Taylor. 1981. A second course in stochastic processes. London: Academic.zbMATHGoogle Scholar
  7. Marks, N.B. 2007. Kolmogorov-Smirnov test statistic and critical values for the Erlang-3 and Erlang-4 distributions. Journal of Applied Statistics 34(8):899–906.MathSciNetCrossRefGoogle Scholar
  8. Skrotzki, W., K. Kegler, R. Tamm, and C.-G. Oertel. 2005. Grain structure and texture of cast iron aluminides. Crystal Research and Technology 40(1/2):90–94. doi: 10.1002/crat.200410311.CrossRefGoogle Scholar
  9. Zeevi, A., and P. Glynn. 2004. Estimating tail decay for stationary sequences via extreme values. Advances in Applied Probability 36(1):198–226.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Indian Statistical Institute 2011

Authors and Affiliations

  1. 1.Indian Statistical Institute, Theoretical Statistics and Mathematics UnitKolkataIndia

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