03541nam a22005295i 4500 978-3-031-61347-0 DE-He213 20251030113103.0 cr nn 008mamaa 240925s2024 sz | s |||| 0|eng d 9783031613470 978-3-031-61347-0 10.1007/978-3-031-61347-0 doi QA276-280 PBT bicssc MAT029000 bisacsh PBT thema Balakrishnan, Narayanaswamy. author. (orcid)0000-0001-5842-8892 https://orcid.org/0000-0001-5842-8892 aut http://id.loc.gov/vocabulary/relators/aut 84941 Sharp Inequalities for Ordered Random Variables in Statistics and Reliability [electronic resource] : Volume I: Standard Order Statistics / by Narayanaswamy Balakrishnan, Tomasz Rychlik. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XIV, 672 p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Frontiers in Probability and the Statistical Sciences, 2624-9995 - 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. The 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. Statistics. 65982 Statistics . 65982 Statistical Theory and Methods. Statistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences. 66911 Rychlik, Tomasz. author. aut http://id.loc.gov/vocabulary/relators/aut 84942 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031613463 Printed edition: 9783031613487 Printed edition: 9783031613494 Frontiers in Probability and the Statistical Sciences, 2624-9995 84943 https://doi.org/10.1007/978-3-031-61347-0 ZDB-2-SMA ZDB-2-SXMS 63679 63679