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Exact distribution of the sample median of a jump type distribution on a bounded domain

Japan Journal of Industrial and Applied Mathematics volume 35, pages 891–913 (2018)Cite this article

Abstract

This paper considers the problem of finding the exact distribution and exact moments of the median of a sample of even size drawn from a jump type distribution with bounded domain in a computable form. The results which are obtained with the help of integral calculus are then applied to two-piece uniform distribution. The exact variances are calculated for both odd and even sample sizes, and efficiency comparisons are made.

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References

  1. Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. Dover Publications, Inc., New York (1972)

    MATH  Google Scholar 

  2. Arnold, B.C., Balakrishnan, N., Nagaraja, H.N.: A first course in order statistics. Wiley, New York (1992)

    MATH  Google Scholar 

  3. Asrabadi, B.R.: The exact confidence interval for the scale parameter and the MVUE of the Laplace distribution. Commun. Stat. Theory Methods 14, 713–733 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bean, M.A.: Probability: the science of uncertainty with applications to investments, insurance, and engineering. Brooks/Cole, Pacific Grove (2001)

    Google Scholar 

  5. Clark, D.R.: A note on the upper-truncated Pareto distribution. Casualty Actuarial Society E-Forum, Winter 2013 (2013). http://www.casact.org/pubs/forum/13wforum/Clark.pdf

  6. Craigmile, P.F., Titterington, D.M.: Parameter estimation for finite mixtures of uniform distributions. Commun. Stat. Theory Methods 26(8), 1981–1995 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cramér, H.: Mathematical methods of statistics. Princeton University Press, Princeton (1946)

    MATH  Google Scholar 

  8. Glickman, T.S., Xu, F.: The distribution of the product of two triangular random variables. Stat. Probab. Lett. 78, 2821–2826 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Gradshteyn, I.S., Ryzhik, I.M.: Table of integrals, series, and products, 7th edn. Academic Press, San Diego (2007)

    MATH  Google Scholar 

  10. Gupta, P.L., Gupta, R.C.: Distribution of a linear function of correlated ordered variables. J. Stat. Plan. Inference 139, 2490–2497 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Gündüz, S., Genç, Aİ.: The distribution of the quotient of two triangularly distributed random variables. Stat. Papers. 56, 291–310 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  12. Hussein, A., Liu, J.: Parametric estimation of mixture of two uniform distributions. J. Stat. Comput. Simul. 79, 395–410 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  13. Karst, O.J., Polowy, H.: Sampling properties of the median of a Laplace distribution. Am. Math. Mon. 70, 628–636 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  14. Klugman, S.A., Panjer, H.H., Willmot, G.E.: Loss models: from data to decisions, 3rd edn. Wiley, New York (2008)

    Book  MATH  Google Scholar 

  15. Lawrence, J.: Distribution of the median in samples from the Laplace distribution. Open J. Stat. 3, 422–426 (2013)

    Article  Google Scholar 

  16. Ma, Y., Chu, H., Mazumdar, M.: Meta-analysis of proportions of rare events-a comparison of exact likelihood methods with robust variance estimation. Commun. Stat. Simul. Comput. 45, 3036–3052 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  17. Nadarajah, S., Bakar, S.A.A.: New composite models for the Danish fire insurance data. Scandinavian Actuarial J. 2014, 180–187 (2014)

    Article  MathSciNet  Google Scholar 

  18. Peck, R.: Statistics: learning from data. Cengage Learning, Boston (2014)

    Google Scholar 

  19. Rohatgi, V.K.: An introduction to probability theory and mathematical statistics. Wiley, New York (1976)

    MATH  Google Scholar 

  20. Stefanescu, S.V.: On the median of a jump type distribution. U.P.B. Sci. Bull. Series A. 71, 9–20 (2009)

    MathSciNet  MATH  Google Scholar 

  21. Wilcox, R.: Modern statistics for the social and behavioral sciences, 2nd edn. CRC Press, Boca Raton (2017)

    MATH  Google Scholar 

  22. Wolfram Research, Inc. (2012) Mathematica, Version 9.0. Champaign, IL

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Acknowledgements

The author thanks the editor, the area editor and the anonymous referee for their comments and suggestions.

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Authors and Affiliations

  1. Department of Statistics, Cukurova University, 01330, Adana, Turkey

    Ali İ. Genç

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  1. Ali İ. Genç
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Correspondence to Ali İ. Genç.

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Genç, A.İ. Exact distribution of the sample median of a jump type distribution on a bounded domain. Japan J. Indust. Appl. Math. 35, 891–913 (2018). https://doi.org/10.1007/s13160-018-0311-2

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  • DOI: https://doi.org/10.1007/s13160-018-0311-2

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