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A characterization by linearity of the regression function based on order statistics

Author

Listed:
  • Balakrishnan, N.
  • Akhundov, I. S.

Abstract

We consider an infinite sequence X1,X2,... of independent random variables having a common continuous distribution function F(x). For 1[less-than-or-equals, slant]i[less-than-or-equals, slant]n, let {Xi:n} denote the ith order statistic among X1,...,Xn. In this paper, we characterize the distributions for which the regression E((X1:n+...+Xn:n)/nXk:n=x) is a linear function of x.

Suggested Citation

  • Balakrishnan, N. & Akhundov, I. S., 2003. "A characterization by linearity of the regression function based on order statistics," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 435-440, July.
    • Handle: RePEc:eee:stapro:v:63:y:2003:i:4:p:435-440
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    Citations

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    Cited by:

    1. M. Jones, 2004. "Families of distributions arising from distributions of order statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 1-43, June.
    2. Ludmila Nevzorova & Valery B.Nevzorov & Ilham Akhundov, 2007. "A simple characterization of Student’s t2 distribution," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 53-57.
    3. Akhundov, I. & Nevzorov, V.B., 2010. "A simple characterization of Student's t3 distribution," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 293-295, March.
    4. Wang, Jiantian, 2011. "A simple characterization of Student's distributions and normal distributions," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 903-906, August.
    5. Huang, Wen-Jang & Su, Nan-Cheng, 2010. "Characterizations based on certain regression assumptions of adjacent order statistics," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1700-1704, December.

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