Stochastic ordering of random kth record values
Dziubdziela, Wiesław ; Tomicka-Stisz, Agata
Applicationes Mathematicae, Tome 26 (1999), p. 293-298 / Harvested from The Polish Digital Mathematics Library
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Let X1,X2,... 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 X1,X2,... 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 Xi.

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:219240 
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     title = {Stochastic ordering of random kth record values},
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     volume = {26},
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Dziubdziela, Wiesław; Tomicka-Stisz, Agata. Stochastic ordering of random kth record values. Applicationes Mathematicae, Tome 26 (1999) pp. 293-298. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv26i3p293bwm/

[000] [1] P. Deheuvels, Strong approximations of kth records and kth record times by Wiener processes, Probab. Theory Related Fields 77 (1988), 195-209. | Zbl 0621.60087

[001] [2] W. Dziubdziela and B. Kopociński, Limiting properties of the k-th record values, Zastos. Mat. 15 (1976), 187-190. | Zbl 0337.60023

[002] [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. | Zbl 0328.60017

[003] [4] Z. Grudzień, On distributions and moments of k-th record statistics with random index, Ann. Univ. Mariae Curie-Skłodowska Sect. A 33 (1979), 99-102.

[004] [5] R. C. Gupta and S. N. U. A. Kirmani, Closure and monotonicity properties of nonhomogeneous Poisson processes and record values, Probab. Engrg. Inform. Sci. 2 (1988), 475-484. | Zbl 1134.60313

[005] [6] U. Kamps, Reliability properties of record values from non-identically distributed random variables, Comm. Statist. Theory Methods 23 (1994), 2101-2112. | Zbl 0825.62193

[006] [7] S. Karlin, Pólya-type distributions, II, Ann. Math. Statist. 28 (1957), 281-308. | Zbl 0080.35605

[007] [8] J. Keilson and U. Sumita, Uniform stochastic ordering and related inequalities, Canad. J. Statist. 10 (1982), 181-198. | Zbl 0516.60063

[008] [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. | Zbl 0844.60061

[009] [10] S. C. Kochar, Some partial ordering results on record values, Comm. Statist. Theory Methods 19 (1990), 299-306. | Zbl 0900.62068

[010] [11] V. B. Nevzorov, Records, Theory Probab. Appl. 32 (1987), 201-228.

[011] [12] M. Shaked and J. G. Shanthikumar, Stochastic Orders and Their Applications, Academic Press, New York, 1994. | Zbl 0806.62009

[012] [13] J. G. Shanthikumar and D. D. Yao, Bivariate characterization of some stochastic order relations, Adv. Appl. Probab. 23 (1991), 642-659. | Zbl 0745.62054