Evaluating improvements of records

Tomasz Rychlik

Applicationes Mathematicae (1997)

  • Volume: 24, Issue: 3, page 315-324
  • ISSN: 1233-7234

Abstract

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We evaluate the extreme differences between the consecutive expected record values appearing in an arbitrary i.i.d. sample in the standard deviation units. We also discuss the relevant estimates for parent distributions coming from restricted families and other scale units.

How to cite

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Rychlik, Tomasz. "Evaluating improvements of records." Applicationes Mathematicae 24.3 (1997): 315-324. <http://eudml.org/doc/219173>.

@article{Rychlik1997,
abstract = {We evaluate the extreme differences between the consecutive expected record values appearing in an arbitrary i.i.d. sample in the standard deviation units. We also discuss the relevant estimates for parent distributions coming from restricted families and other scale units.},
author = {Rychlik, Tomasz},
journal = {Applicationes Mathematicae},
keywords = {monotone failure rate; monotone failure probability; record value; projection; sharp bound; variance; central absolute moment; independent identically distributed variables},
language = {eng},
number = {3},
pages = {315-324},
title = {Evaluating improvements of records},
url = {http://eudml.org/doc/219173},
volume = {24},
year = {1997},
}

TY - JOUR
AU - Rychlik, Tomasz
TI - Evaluating improvements of records
JO - Applicationes Mathematicae
PY - 1997
VL - 24
IS - 3
SP - 315
EP - 324
AB - We evaluate the extreme differences between the consecutive expected record values appearing in an arbitrary i.i.d. sample in the standard deviation units. We also discuss the relevant estimates for parent distributions coming from restricted families and other scale units.
LA - eng
KW - monotone failure rate; monotone failure probability; record value; projection; sharp bound; variance; central absolute moment; independent identically distributed variables
UR - http://eudml.org/doc/219173
ER -

References

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  1. [1] M. Ahsanullah, Linear predictions of record values for two parameter exponential distribution, Ann. Inst. Statist. Math. 32 (1980), 363-368. 
  2. [2] A. V. Balakrishnan, Applied Functional Analysis, 2nd ed., Springer, New York, 1981. Zbl0459.46014
  3. [3] I. R. Dunsmore, The future occurrence of records, Ann. Inst. Statist. Math. 35 (1983), Part A, 267-277. Zbl0522.62027
  4. [4] L. Gajek and T. Rychlik, Projection method for moment bounds on order statistics from restricted families. I. Dependent case, J. Multivariate Anal. 57 (1996), 156-174. Zbl0863.62045
  5. [5] S. Moriguti, A modification of Schwarz's inequality with applications to distributions, Ann. Math. Statist. 24 (1953), 107-113. Zbl0050.35301
  6. [6] H. N. Nagaraja, On the expected values of record values, Austral. J. Statist. 20 (1978), 176-182. Zbl0407.62025
  7. [7] V. B. Nevzorov, Records, Teor. Veroyatnost. i Primenen. 32 (1987), 219-251 (in Russian). 
  8. [8] W. R. van Zwet, Convex Transformations of Random Variables, Mathematisch Centrum, Amsterdam, 1964. Zbl0125.37102

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