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020 _a9783031613470
_9978-3-031-61347-0
024 7 _a10.1007/978-3-031-61347-0
_2doi
050 4 _aQA276-280
072 7 _aPBT
_2bicssc
072 7 _aMAT029000
_2bisacsh
072 7 _aPBT
_2thema
100 1 _aBalakrishnan, Narayanaswamy.
_eauthor.
_0(orcid)0000-0001-5842-8892
_1https://orcid.org/0000-0001-5842-8892
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_984941
245 1 0 _aSharp Inequalities for Ordered Random Variables in Statistics and Reliability
_h[electronic resource] :
_bVolume I: Standard Order Statistics /
_cby Narayanaswamy Balakrishnan, Tomasz Rychlik.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXIV, 672 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aFrontiers in Probability and the Statistical Sciences,
_x2624-9995
505 0 _a- Introduction and Notation -- Analytic Inequalities and Other Tools -- Deterministic Bounds -- General, Symmetric and Life IID Samples -- Sampling from Finite Populations -- IID Samples from Shape Restricted Families.
520 _aThe book discusses various inequalities and sharp bounds for the usual order statistics as well as some functions of them. In particular, deterministic bounds, bounds for the case of IID samples from general, symmetric and life distributions, IID samples from shape restricted family of distributions, and samples from finite populations are all discussed in detail. An elaborate numerical evaluation and comparison of various bounds are also presented in order to illustrate their inherent differences as well as their precision. Furthermore, their applications to inference, reliability theory and characterizations are also highlighted. The book provides an in-depth exposure to various mathematical inequalities and bounds established historically as well as in recent years and their applications to order statistics and some important functions of them. It thus presents an up-to-date discussion of all results in this important area of mathematical and statistical research. The results described here are general in nature and therefore could be useful in other areas of Probability and Statistics as well.
650 0 _aStatistics.
_965982
650 0 _aStatistics .
_965982
650 1 4 _aStatistical Theory and Methods.
650 2 4 _aStatistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences.
_966911
700 1 _aRychlik, Tomasz.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_984942
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031613463
776 0 8 _iPrinted edition:
_z9783031613487
776 0 8 _iPrinted edition:
_z9783031613494
830 0 _aFrontiers in Probability and the Statistical Sciences,
_x2624-9995
_984943
856 4 0 _uhttps://doi.org/10.1007/978-3-031-61347-0
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c63679
_d63679