LEADER 03455nam 22006015 450 001 9910890179503321 005 20250523135531.0 010 $a3-031-61347-3 024 7 $a10.1007/978-3-031-61347-0 035 $a(MiAaPQ)EBC31690015 035 $a(Au-PeEL)EBL31690015 035 $a(CKB)36193817100041 035 $a(DE-He213)978-3-031-61347-0 035 $a(OCoLC)1459141772 035 $a(EXLCZ)9936193817100041 100 $a20240925d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSharp Inequalities for Ordered Random Variables in Statistics and Reliability $eVolume I: Standard Order Statistics /$fby Narayanaswamy Balakrishnan, Tomasz Rychlik 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (681 pages) 225 1 $aFrontiers in Probability and the Statistical Sciences,$x2624-9995 311 08$a3-031-61346-5 327 $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. 330 $aThe book discusses various inequalities and sharp bounds for the usual order statistics as well as some functions of them. In particular, deterministic bounds, bounds for the case of IID samples from general, symmetric and life distributions, IID samples from shape restricted family of distributions, and samples from finite populations are all discussed in detail. An elaborate numerical evaluation and comparison of various bounds are also presented in order to illustrate their inherent differences as well as their precision. Furthermore, their applications to inference, reliability theory and characterizations are also highlighted. The book provides an in-depth exposure to various mathematical inequalities and bounds established historically as well as in recent years and their applications to order statistics and some important functions of them. It thus presents an up-to-date discussion of all results in this important area of mathematical and statistical research. The results described here are general in nature and therefore could be useful in other areas of Probability and Statistics as well. 410 0$aFrontiers in Probability and the Statistical Sciences,$x2624-9995 606 $aStatistics 606 $aStatistics 606 $aStatistical Theory and Methods 606 $aStatistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences 606 $aDesigualtats (Matemàtica)$2thub 606 $aEstadística d'ordre$2thub 608 $aLlibres electrònics$2thub 615 0$aStatistics. 615 0$aStatistics. 615 14$aStatistical Theory and Methods. 615 24$aStatistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences. 615 7$aDesigualtats (Matemàtica) 615 7$aEstadística d'ordre 676 $a519.2 700 $aBalakrishnan$b Narayanaswamy$0541916 701 $aRychlik$b Tomasz$01770318 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910890179503321 996 $aSharp Inequalities for Ordered Random Variables in Statistics and Reliability$94249099 997 $aUNINA