05568nam 2200721 450 991083086930332120230607223656.01-283-28127-997866132812721-118-15046-51-118-15045-7(CKB)2550000000060220(EBL)818797(SSID)ssj0000608308(PQKBManifestationID)11413996(PQKBTitleCode)TC0000608308(PQKBWorkID)10590529(PQKB)11620434(MiAaPQ)EBC818797(OCoLC)761321893(EXLCZ)99255000000006022020160816h20022002 uy 0engur|n|---|||||txtccrRuns and scans with applications /N. Balakrishnan, Markos V. KoutrasNew York :John Wiley & Sons, Inc.,2002.©20021 online resource (484 p.)Wiley Series in Probability and StatisticsDescription based upon print version of record.0-471-24892-4 Includes bibliographical references and indexes.Runs and Scans with Applications; Contents; List of Tables; List of Figures; Preface; 1 Introduction and Historical Remarks; 1.1 WHAT ARE RUNS?; 1.2 WHY RUNS?; 1.3 WHAT USE ARE RUNS?; 1.4 FROM RUNS TO SCANS; 1.5 WHAT TO EXPECT; 2 Waiting for the First Run Occurrence; 2.1 INTRODUCTION; 2.2 I.I.D. TRIALS - GEOMETRIC DISTRIBUTION OF ORDER k; 2.2.1 Distribution Function; 2.2.2 Generating Functions and Moments; 2.2.3 Bounds and Approximations; 2.2.4 Properties; 2.2.5 Asymptotics; 2.2.6 Estimation; 2.3 MARKOV-DEPENDENT TRIALS - MARKOV-GEOMETRIC DISTRIBUTION OF ORDER k2.4 NONIDENTICAL TRIALS - INTERVENED GEOMETRIC DISTRIBUTION OF ORDER k2.5 BINARY SEQUENCE OF ORDER l - EXTENDED GEOMETRIC DISTRIBUTION OF ORDER k; 2.6 CONDITIONAL DISTRIBUTIONS; 2.7 OTHER RELATED DISTRIBUTIONS; 2.8 MISCELLANEA; 3 Applications; 3.1 INTRODUCTION; 3.2 RELIABILITY THEORY; 3.3 PSYCHOLOGY, ECOLOGY AND METEOROLOGY; 3.4 RANDOMNESS TESTS; 3.5 START-UP DEMONSTRATION TESTS; 3.6 STATISTICAL QUALITY CONTROL; 3.7 MISCELLANEOUS APPLICATIONS; 4 Waiting for Multiple Run Occurrences; 4.1 INTRODUCTION; 4.2 I.I.D. TRIALS-NEGATIVE BINOMIAL DISTRIBUTIONS OF ORDERS k; 4.2.1 Distribution Function4.2.2 Generating Functions and Moments4.2.3 Properties; 4.2.4 Asymptotics; 4.2.5 Estimation; 4.3 MARKOV-DEPENDENT TRIALS- MARKOV-NEGATIVE BINOMIAL DISTRIBUTIONS OF ORDER k; 4.4 MISCELLANEA; 5 Number of Run Occurrences; 5.1 INTRODUCTION; 5.2 I.I.D. TRIALS-BINOMIAL DISTRIBUTIONS OF ORDER k; 5.2.1 Distribution Function; 5.2.2 Generating Functions and Moments; 5.2.3 Bounds and Approximations; 5.2.4 Asymptotics; 5.2.5 Estimation; 5.3 MARKOV-DEPENDENT TRIALS-MARKOV-BINOMIAL DISTRIBUTIONS OF ORDER k; 5.4 CONDITIONAL DISTRIBUTIONS; 5.5 OTHER RELATED DISTRIBUTIONS; 6 Sooner/Later Run Occurrences6.1 INTRODUCTION6.2 I.I.D. TRIALS - SOONER/LATER GEOMETRIC DISTRIBUTIONS OF ORDER (k1, k2); 6.2.1 Distribution Function; 6.2.2 Generating Functions and Moments; 6.2.3 Bounds and Asymptotics; 6.3 MARKOV-DEPENDENT TRIALS - SOONER/LATER MARKOV-GEOMETRIC DISTRIBUTION OF ORDER {k1, k2); 6.4 BINARY SEQUENCE OF ORDER I - EXTENDED SOONER/LATER GEOMETRIC DISTRIBUTION OF ORDER (k1, k2); 6.5 CONDITIONAL DISTRIBUTION; 6.6 OTHER RELATED DISTRIBUTIONS; 6.7 MISCELLANEA; 7 Multivariate Run-Related Distributions; 7.1 INTRODUCTION; 7.2 I.I.D. TRIALS-TRINOMIAL DISTRIBUTIONS OF ORDER (k1, k2)7.2.1 Distribution Function7.2.2 Generating Functions and Moments; 7.3 MARKOV-DEPENDENT TRIALS- MARKOV-TRINOMIAL DISTRIBUTIONS OF ORDER (k1, k2); 7.4 MISCELLANEA; 8 Applications; 8.1 INTRODUCTION; 8.2 MACHINE MAINTENANCE; 8.3 LEARNING MODELS; 8.4 BRAND SWITCHING MODELS; 8.5 CLIMATOLOGY; 8.6 START-UP DEMONSTRATION TESTS WITH REJECTION OF UNITS UPON OBSERVING l FAILURES; 8.7 TWO-STAGE START-UP DEMONSTRATION TESTING; 8.8 VOLLEYBALL SCORES ANALYSIS; 8.9 NON-PARAMETRIC TESTS FOR RANDOMNESS; 8.10 MISCELLANEOUS APPLICATIONS; 9 Waiting for the First Scan; 9.1 INTRODUCTION; 9.2 I.I.D. TRIALS9.2.1 Distribution FunctionExpert practical and theoretical coverage of runs and scansThis volume presents both theoretical and applied aspects of runs and scans, and illustrates their important role in reliability analysis through various applications from science and engineering. Runs and Scans with Applications presents new and exciting content in a systematic and cohesive way in a single comprehensive volume, complete with relevant approximations and explanations of some limit theorems.The authors provide detailed discussions of both classical and current problems, such as:* Sooner and later waiting timeWiley series in probability and statistics.ProbabilitiesSequences (Mathematics)Pattern perceptionCombinatorial analysisReliability (Engineering)Probabilities.Sequences (Mathematics)Pattern perception.Combinatorial analysis.Reliability (Engineering)519.2Balakrishnan N.1956-103508Koutras Markos V.MiAaPQMiAaPQMiAaPQBOOK9910830869303321Runs and scans with applications4063812UNINA