The geometric process and its applications / Yeh Lam.

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.

"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.

Machine converted from AACR2 source record.