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Analysis of order statistics from distributions with regularly varying tails. (English) Zbl 1311.60026

In this article, the authors study some stochastics orders of order statistics from distributions with regular variation tails. They prove the similar results to C. Kleiber [Stat. Probab. Lett. 58, No. 4, 381–388 (2002; Zbl 1014.62058)] for independent but not necessarily identically distributed random variables without the monotone restrictions on the density functions. Order statistics from two samples are also discussed. A sufficient and necessary condition for stochastically comparing order statistics on the right tails is given.
Finally, extensions to coherent systems are mentioned.

MSC:

60E15 Inequalities; stochastic orderings
60K10 Applications of renewal theory (reliability, demand theory, etc.)
62G30 Order statistics; empirical distribution functions

Citations:

Zbl 1014.62058
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References:

[1] Balakrishnan N., Revista Matemática Complutense 20 pp 7– (2007) · Zbl 1148.62031 · doi:10.5209/rev_REMA.2007.v20.n1.16528
[2] Barlow R.E., Statistical Theory of Reliability and Life Testing (1981)
[3] DOI: 10.1017/CBO9780511721434 · doi:10.1017/CBO9780511721434
[4] DOI: 10.1239/jap/1059060898 · Zbl 1046.62111 · doi:10.1239/jap/1059060898
[5] DOI: 10.1002/0471722162 · Zbl 1053.62060 · doi:10.1002/0471722162
[6] DOI: 10.1007/978-3-642-33483-2 · doi:10.1007/978-3-642-33483-2
[7] DOI: 10.1016/S0167-7152(02)00151-7 · Zbl 1014.62058 · doi:10.1016/S0167-7152(02)00151-7
[8] DOI: 10.1016/S0378-3758(02)00495-0 · Zbl 1032.60013 · doi:10.1016/S0378-3758(02)00495-0
[9] Kochar S., J. Iran. Statist. Soc. 6 pp 125– (2007)
[10] DOI: 10.1239/jap/1245676091 · Zbl 1168.60318 · doi:10.1239/jap/1245676091
[11] DOI: 10.1017/S0269964809990258 · Zbl 1193.60025 · doi:10.1017/S0269964809990258
[12] DOI: 10.1002/nav.20251 · Zbl 1136.62066 · doi:10.1002/nav.20251
[13] DOI: 10.1007/s00184-007-0133-8 · Zbl 1357.62304 · doi:10.1007/s00184-007-0133-8
[14] Nolan J.P., Stable distributions-Models for heavy tailed data (2011)
[15] Resnick S.I., Heavy-Tail Phenomena: Probabilistic and Statistical Modeling (2007) · Zbl 1152.62029
[16] DOI: 10.1214/aos/1176348541 · Zbl 0745.62011 · doi:10.1214/aos/1176348541
[17] DOI: 10.1016/0167-7152(93)90166-G · Zbl 0774.62013 · doi:10.1016/0167-7152(93)90166-G
[18] DOI: 10.1007/978-0-387-34675-5 · Zbl 1111.62016 · doi:10.1007/978-0-387-34675-5
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