TY  - BOOK
AU  - Lam,Yeh
TI  - The geometric process and its applications
SN  - 981270003X
AV  - QA274 .L35 2007
U1  - 519.23 22
PY  - 2007///]
CY  - Hackensack, NJ
PB  - World Scientific
KW  - Stochastic processes
KW  - Renewal theory
N1  - Includes bibliographical references and index; 1.2; The Poisson Process; 2 --; 1.3; The Renewal Process; 8 --; 1.4; Stochastic Order and Class of Lifetime Distributions; 18 --; 1.5; Martingales; 26 --; 1.6; The Rate of Occurrence of Failures; 31 --; 2; Geometric Process; 37 --; 2.2; Geometric Process; 37 --; 2.3; Age, Residual Life and Total Life; 42 --; 2.4; Limit Theorems for Geometric Process; 45 --; 2.5; A Geometric Process with Exponential Distribution; 50 --; 3; Geometric Function; 55 --; 3.2; Geometric Equation; 56 --; 3.3; Existence of Geometric Function; 57 --; 3.4; General Solution to Geometric Equation; 61 --; 3.5; Analytic Solution to Geometric Equation; 63 --; 3.6; Numerical Solution to Geometric Equation; 79 --; 3.7; Approximate Solution to Geometric Equation; 83 --; 3.8; Comparison with Simulation Solution to Geometric Equation; 89 --; 3.9; Exponential Distribution Case; 98 --; 4; Statistical Inference of Geometric Process; 101 --; 4.2; Hypothesis Testing for Geometric Process; 101 --; 4.3; Estimation of Parameters in Geometric Process; 104 --; 4.4; Asymptotic Distributions of the Estimators; 106 --; 4.5; Parametric Inference for Geometric Process; 113 --; 5; Application of Geometric Process to Data Analysis; 121 --; 5.2; Data Analysis by Geometric Process Model; 122 --; 5.3; Data Analysis by Poisson Process Models; 123 --; 5.4; Real Data Analysis and Comparison; 125 --; 5.5; Analysis of Data by a Threshold Geometric Process Model; 142 --; 6; Geometric Process Maintenance Model; 155 --; 6.2; A Geometric Process Maintenance Model; 156 --; 6.3; Optimal Replacement Policy; 161 --; 6.4; Monotonicity of the Optimal Policy for a Deteriorating System; 164 --; 6.5; A Monotone Process Model for a Multistate System; 168 --; 6.6; A Geometric Process Shock Model; 182 --; 6.7; A Geometric Process [delta]-Shock Model; 193 --; 6.8; A Threshold Geometric Process Maintenance Model; 201 --; 6.9; A Geometric Process Preventive Maintenance Model; 210 --; 7; Application to Analysis of System Reliability; 227 --; 7.2; Reliability Analysis for a Series System; 227 --; 7.3; Reliability Analysis for a Parallel System; 234 --; 7.4; Reliability Analysis for a Cold Standby System; 239 --; 7.5; A Geometric Process Maintenance Model for a Cold Standby System; 249 --; 8; Applications of Geometric Process to Operational Research; 255 --; 8.2; A Geometric Process M/M/1 Queueing Model; 255 --; 8.3; A Geometric Process Warranty Model; 274 --; Appendix; A SARS Data Sets; 286 --; A.1; Hong Kong SARS Daily Infected Case Data; 286 --; A.2; Singapore SARS Daily Infected Case Data; 287 --; A.3; Ontario SARS Daily Infected Case Data; 288 --; A.4; Taiwan SARS Daily Infected Case Data; 289
N2  - "A geometric process is a simple monotone process that was first introduced by the author in 1988. It is a generalization of renewal process. This book captures the extensive research work on geometric processes that has been done since then in both probability and statistics theory and various applications. Some results are published for the first time." "A reference book for researchers and a handbook for practioners, it is also a useful textbook for postgraduate or senior undergraduate students."--Jacket
ER  -