LEADER 05410nam 2200661 450 001 9910830587903321 005 20230421050615.0 010 $a1-283-28125-2 010 $a9786613281258 010 $a1-118-15041-4 010 $a1-118-15040-6 035 $a(CKB)2550000000060218 035 $a(EBL)818795 035 $a(SSID)ssj0000555390 035 $a(PQKBManifestationID)11385983 035 $a(PQKBTitleCode)TC0000555390 035 $a(PQKBWorkID)10518626 035 $a(PQKB)10994340 035 $a(MiAaPQ)EBC818795 035 $a(OCoLC)761319822 035 $a(EXLCZ)992550000000060218 100 $a20160815h19981998 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aRecords /$fBarry C. Arnold, N. Balakrishnan, H.N. Nagaraja 210 1$aNew York :$cJohn Wiley & Sons, Inc.,$d1998. 210 4$dİ1998 215 $a1 online resource (342 p.) 225 1 $aWiley Series in Probability and Statistics. Probability and Statistics Section 300 $a"A Wiley-Interscience Publication." 311 $a0-471-08108-6 320 $aIncludes bibliographical references and indexes. 327 $aRecords; Contents; Notations and Abbreviations; Preface; 1. Introduction; 1.1 Who Cares?; 1.2 A Road Map; 2. Basic Distributional Results; 2.1 Introduction; 2.2 Standard Record Values Processes; 2.3 Record Values From the Classical Model; 2.4 Record Values From Specific Distributions; 2.4.1 Weibull Records; 2.4.2 Power Function Distribution Records; 2.4.3 Pareto Records; 2.4.4 Extreme Value Records; 2.5 Record Times and Related Statistics; 2.6 Markov Chains; 2.7 Moments of Record Values; 2.7.1 Weibull Distribution; 2.7.2 Power Function Distribution; 2.7.3 Pareto Distribution 327 $a2.7.4 Extreme Value Distribution2.7.5 Normal Distribution; 2.7.6 Covariance and Correlations; 2.8 A Discrete Interlude; 2.9 Geometric Results; 2.10 Counting Process and k-Records; 2.10.1 A Point Process View; 2.10.2 k-Record Statistics; Exercises; 3. Moment Relations Bounds and Approximations; 3.1 Introduction; 3.2 Exponential Distribution; 3.3 Weibull Distribution; 3.4 Gumbel Distribution; 3.5 Lomax Distribution; 3.6 Normal Distribution; 3.7 Logistic Distribution; 3.8 Bounds and Approximations; 3.9 Results for k-Records; Exercises; 4. Characterizations; 4.1 Introduction 327 $a4.2 Characterizing Properties of Record Values4.2.1 The Moment Sequence; 4.2.2 Regression of Adjacent Record Values; 4.3 Families of Distributions; 4.3.1 Families Defined by Reliability Properties; 4.3.2 Linear Regressions of Adjacent Record Values; 4.4 The Exponential Distribution; 4.4.1 The Incomplete Catalog; 4.4.2 Integrated Cauchy Functional Equation; 4.4.3 Characterizations Based on the ICFE and Other Functional Equations; 4.4.4 Lower Record Statistics; 4.5 Other Continuous Distributions; 4.6 Geometric-Tail Distributions; 4.7 Dependence Structures of Record Values and Order Statistics 327 $aExercises5. Inference; 5.1 Introduction; 5.2 Maximum Likelihood Estimation; 5.3 Best Linear Unbiased Estimation; 5.4 Best Linear Invariant Estimation; 5.5 Interval Estimation and Tests of Hypotheses; 5.6 Point Prediction; 5.6.1 Best Linear Unbiased Prediction; 5.6.2 Best Linear Invariant Prediction; 5.6.3 Asymptotic Linear Prediction; 5.7 Interval Prediction; 5.7.1 Prediction Intervals Based on BLUE's; 5.7.2 Conditional Prediction Intervals; 5.7.3 Tolerance Region Prediction; 5.7.4 Bayesian Prediction Intervals; 5.8 Illustrative Examples; 5.9 Inference with Records and Inter-Record Times 327 $a5.10 Distribution-Free Tests in Time-Series Using RecordsExercises; 6. General Record Models; 6.1 Introduction; 6.2 Geometrically Increasing Populations; 6.3 The F? Record Model; 6.3.1 Finite-sample Properties; 6.3.2 Asymptotic Properties; 6.4 Linear Drift Record Model; 6.5 The Pfeifer Model; 6.6 Characterizations; 6.6.1 F? and Linear Drift Record Models; 6.6.2 The Pfeifer Model; 6.7 Records From Dependent Sequences; 6.7.1 Markov Sequences; 6.7.2 Exchangeable Observations; 6.7.3 Dependent Models Based on Archimedean Copula; 6.7.4 A Random Power Record Model; Exercises 327 $a7. Random and Point Process Record Models 330 $aThe first and only comprehensive guide to modern record theory and its applicationsAlthough it is often thought of as a special topic in order statistics, records form a unique area, independent of the study of sample extremes. Interest in records has increased steadily over the years since Chandler formulated the theory of records in 1952. Numerous applications of them have been developed in such far-flung fields as meteorology, sports analysis, hydrology, and stock market analysis, to name just a few. And the literature on the subject currently comprises papers and journal articles n 410 0$aWiley series in probability and statistics.$pProbability and statistics. 606 $aOrder statistics 606 $aWorld records 615 0$aOrder statistics. 615 0$aWorld records. 676 $a519.5 700 $aArnold$b Barry C.$068522 702 $aBalakrishnan$b N.$f1956- 702 $aNagaraja$b H. N$g(Haikady Navada),$f1954- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910830587903321 996 $aRecords$94086143 997 $aUNINA