LEADER 05227nam 22008535 450 001 9910438034103321 005 20250411131904.0 010 $a0-8176-8361-5 024 7 $a10.1007/978-0-8176-8361-0 035 $a(CKB)3710000000015695 035 $a(EBL)1030320 035 $a(OCoLC)857364786 035 $a(SSID)ssj0000988260 035 $a(PQKBManifestationID)11627770 035 $a(PQKBTitleCode)TC0000988260 035 $a(PQKBWorkID)10971179 035 $a(PQKB)10734804 035 $a(DE-He213)978-0-8176-8361-0 035 $a(MiAaPQ)EBC6315427 035 $a(MiAaPQ)EBC1030320 035 $a(Au-PeEL)EBL1030320 035 $a(CaPaEBR)ebr10976194 035 $a(PPN)172416809 035 $a(EXLCZ)993710000000015695 100 $a20130823d2013 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aQuantile-Based Reliability Analysis /$fby N. Unnikrishnan Nair, P.G. Sankaran, N. Balakrishnan 205 $a1st ed. 2013. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Birkhäuser,$d2013. 215 $a1 online resource (411 p.) 225 1 $aStatistics for Industry and Technology,$x2364-625X 300 $aDescription based upon print version of record. 311 08$a0-8176-8360-7 320 $aIncludes bibliographical references (pages 361-383) and index. 327 $aPreface -- Chapter I Quantile Functions -- Chapter II Quantile-Based Reliability Concepts -- Chapter III Quantile Function Models -- Chapter IV Ageing Concepts -- Chapter V Total Time on Test Transforms (TTT) -- Chapter VI L-Moments of Residual Life and Partial Moments -- Chapter VII Nonmonotone Hazard Quantile Functions -- Chapter VIII Stochastic Orders in Reliability -- IX Estimation and Modeling.- References -- Index. 330 $aQuantile-Based Reliability Analysis presents a novel approach to reliability theory using quantile functions in contrast to the traditional approach based on distribution functions. Quantile functions and distribution functions are mathematically equivalent ways to define a probability distribution. However, quantile functions have several advantages over distribution functions. First, many data sets with non-elementary distribution functions can be modeled by quantile functions with simple forms. Second, most quantile functions approximate many of the standard models in reliability analysis quite well. Consequently, if physical conditions do not suggest a plausible model, an arbitrary quantile function will be a good first approximation. Finally, the inference procedures for quantile models need less information and are more robust to outliers.   Quantile-Based Reliability Analysis?s innovative methodology is laid out in a well-organized sequence of topics, including:   ·       Definitions and properties of reliability concepts in terms of quantile functions; ·       Ageing concepts and their interrelationships; ·       Total time on test transforms; ·       L-moments of residual life; ·       Score and tail exponent functions and relevant applications; ·       Modeling problems and stochastic orders connecting quantile-based reliability functions.   An ideal text for advanced undergraduate and graduate courses in reliability and statistics, Quantile-Based Reliability Analysis also contains many unique topics for study and research in survival analysis, engineering, economics, and the medical sciences. In addition, its illuminating discussion of the general theory of quantile functions is germane to many contexts involving statistical analysis.  . 410 0$aStatistics for Industry and Technology,$x2364-625X 606 $aStatistics 606 $aProbabilities 606 $aStatistics 606 $aBiometry 606 $aMathematical models 606 $aStatistical Theory and Methods 606 $aProbability Theory 606 $aStatistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences 606 $aStatistics in Business, Management, Economics, Finance, Insurance 606 $aBiostatistics 606 $aMathematical Modeling and Industrial Mathematics 615 0$aStatistics. 615 0$aProbabilities. 615 0$aStatistics. 615 0$aBiometry. 615 0$aMathematical models. 615 14$aStatistical Theory and Methods. 615 24$aProbability Theory. 615 24$aStatistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences. 615 24$aStatistics in Business, Management, Economics, Finance, Insurance. 615 24$aBiostatistics. 615 24$aMathematical Modeling and Industrial Mathematics. 676 $a519.287 700 $aNair$b N. Unnikrishnan$4aut$4http://id.loc.gov/vocabulary/relators/aut$0861199 702 $aSankaran$b P.G$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aBalakrishnan$b N$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438034103321 996 $aQuantile-Based Reliability Analysis$92508213 997 $aUNINA