LEADER 05568nam 2200721 450 001 9910830869303321 005 20230607223656.0 010 $a1-283-28127-9 010 $a9786613281272 010 $a1-118-15046-5 010 $a1-118-15045-7 035 $a(CKB)2550000000060220 035 $a(EBL)818797 035 $a(SSID)ssj0000608308 035 $a(PQKBManifestationID)11413996 035 $a(PQKBTitleCode)TC0000608308 035 $a(PQKBWorkID)10590529 035 $a(PQKB)11620434 035 $a(MiAaPQ)EBC818797 035 $a(OCoLC)761321893 035 $a(EXLCZ)992550000000060220 100 $a20160816h20022002 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aRuns and scans with applications /$fN. Balakrishnan, Markos V. Koutras 210 1$aNew York :$cJohn Wiley & Sons, Inc.,$d2002. 210 4$dİ2002 215 $a1 online resource (484 p.) 225 1 $aWiley Series in Probability and Statistics 300 $aDescription based upon print version of record. 311 $a0-471-24892-4 320 $aIncludes bibliographical references and indexes. 327 $aRuns 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 k 327 $a2.4 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 Function 327 $a4.2.2 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 Occurrences 327 $a6.1 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) 327 $a7.2.1 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. TRIALS 327 $a9.2.1 Distribution Function 330 $aExpert practical and theoretical coverage of runs and scansThis volume presents both theoretical and applied aspects of runs and scans, and illustrates their important role in reliability analysis through various applications from science and engineering. Runs and Scans with Applications presents new and exciting content in a systematic and cohesive way in a single comprehensive volume, complete with relevant approximations and explanations of some limit theorems.The authors provide detailed discussions of both classical and current problems, such as:* Sooner and later waiting time 410 0$aWiley series in probability and statistics. 606 $aProbabilities 606 $aSequences (Mathematics) 606 $aPattern perception 606 $aCombinatorial analysis 606 $aReliability (Engineering) 615 0$aProbabilities. 615 0$aSequences (Mathematics) 615 0$aPattern perception. 615 0$aCombinatorial analysis. 615 0$aReliability (Engineering) 676 $a519.2 700 $aBalakrishnan$b N.$f1956-$0103508 702 $aKoutras$b Markos V. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910830869303321 996 $aRuns and scans with applications$94063812 997 $aUNINA