Stochastic ordering of random kth record values

Wiesław Dziubdziela; Agata Tomicka-Stisz

Applicationes Mathematicae (1999)

  • Volume: 26, Issue: 3, page 293-298
  • ISSN: 1233-7234

Abstract

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Let X 1 , X 2 , . . . be a sequence of independent and identically distributed random variables with continuous distribution function F(x). Denote by X(1,k),X(2,k),... the kth record values corresponding to X 1 , X 2 , . . . We obtain some stochastic comparison results involving the random kth record values X(N,k), where N is a positive integer-valued random variable which is independent of the X i .

How to cite

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Dziubdziela, Wiesław, and Tomicka-Stisz, Agata. "Stochastic ordering of random kth record values." Applicationes Mathematicae 26.3 (1999): 293-298. <http://eudml.org/doc/219240>.

@article{Dziubdziela1999,
abstract = {Let $X_1,X_2,...$ be a sequence of independent and identically distributed random variables with continuous distribution function F(x). Denote by X(1,k),X(2,k),... the kth record values corresponding to $X_1,X_2,...$ We obtain some stochastic comparison results involving the random kth record values X(N,k), where N is a positive integer-valued random variable which is independent of the $X_i$.},
author = {Dziubdziela, Wiesław, Tomicka-Stisz, Agata},
journal = {Applicationes Mathematicae},
keywords = {stochastic comparison; likelihood ratio order; extreme value theory; hazard rate order; k-record values; random k-record values; random sums; -record values; random -record values},
language = {eng},
number = {3},
pages = {293-298},
title = {Stochastic ordering of random kth record values},
url = {http://eudml.org/doc/219240},
volume = {26},
year = {1999},
}

TY - JOUR
AU - Dziubdziela, Wiesław
AU - Tomicka-Stisz, Agata
TI - Stochastic ordering of random kth record values
JO - Applicationes Mathematicae
PY - 1999
VL - 26
IS - 3
SP - 293
EP - 298
AB - Let $X_1,X_2,...$ be a sequence of independent and identically distributed random variables with continuous distribution function F(x). Denote by X(1,k),X(2,k),... the kth record values corresponding to $X_1,X_2,...$ We obtain some stochastic comparison results involving the random kth record values X(N,k), where N is a positive integer-valued random variable which is independent of the $X_i$.
LA - eng
KW - stochastic comparison; likelihood ratio order; extreme value theory; hazard rate order; k-record values; random k-record values; random sums; -record values; random -record values
UR - http://eudml.org/doc/219240
ER -

References

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  1. [1] P. Deheuvels, Strong approximations of kth records and kth record times by Wiener processes, Probab. Theory Related Fields 77 (1988), 195-209. Zbl0621.60087
  2. [2] W. Dziubdziela and B. Kopociński, Limiting properties of the k-th record values, Zastos. Mat. 15 (1976), 187-190. Zbl0337.60023
  3. [3] W. Freudenberg and D. Szynal, Limit laws for a random number of record values, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 24 (1976), 193-199. Zbl0328.60017
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  7. [7] S. Karlin, Pólya-type distributions, II, Ann. Math. Statist. 28 (1957), 281-308. Zbl0080.35605
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  9. [9] S. N. U. A. Kirmani and R. C. Gupta, Some results on randomly stopped minimal repair processes, Comm. Statist. Stochastic Models 11 (1995), 631-644. Zbl0844.60061
  10. [10] S. C. Kochar, Some partial ordering results on record values, Comm. Statist. Theory Methods 19 (1990), 299-306. Zbl0900.62068
  11. [11] V. B. Nevzorov, Records, Theory Probab. Appl. 32 (1987), 201-228. 
  12. [12] M. Shaked and J. G. Shanthikumar, Stochastic Orders and Their Applications, Academic Press, New York, 1994. Zbl0806.62009
  13. [13] J. G. Shanthikumar and D. D. Yao, Bivariate characterization of some stochastic order relations, Adv. Appl. Probab. 23 (1991), 642-659. Zbl0745.62054

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