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Applied Probability and Stochastic Processes
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Applied Probability and Stochastic Processes
von: Richard M. Feldman, Ciriaco Valdez-Flores
Springer-Verlag, 2009
ISBN: 9783642051586
400 Seiten, Download: 3083 KB
 
Format:  PDF
geeignet für: Apple iPad, Android Tablet PC's Online-Lesen PC, MAC, Laptop

Typ: B (paralleler Zugriff)

 

 
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Inhaltsverzeichnis

  Preface 6  
  Contents 9  
  Basic Probability Review 14  
     Basic Definitions 14  
     Random Variables and Distribution Functions 17  
     Mean and Variance 23  
     Important Distributions 26  
     Multivariate Distributions 36  
     Combinations of Random Variables 44  
        Fixed Sum of Random Variables 45  
        Random Sum of Random Variables 45  
        Mixtures of Random Variables 47  
     Appendix 48  
     Problems 50  
     References 56  
  Basics of Monte Carlo Simulation 57  
     Simulation by Hand 58  
     Generation of Random Numbers 61  
        Multiplicative Linear Congruential Generators 62  
        A Multiple Recursive Generator 64  
        Composite Generators 65  
     Generation of Random Variates 67  
        Discrete Random Variates 67  
        Continuous Random Variates 73  
        Bivariate Continuous Random Variates 76  
        Random Variates from Empirical Distributions 78  
     Appendix 79  
     Problems 81  
     References 84  
  Basic Statistical Review 85  
     Collection of Data 85  
        Preliminary Definitions 86  
        Graphical Representations 87  
     Parameter Estimation 90  
        Method of Moments 92  
        Maximum Likelihood Estimation 93  
     Confidence Intervals 94  
        Means 95  
        Proportions 99  
        Variances 99  
        Correlation Coefficient 101  
     Fitting Distributions 102  
        The Chi-Square Test 103  
        The Kolmogorov-Smirnov Test 107  
     Fitting Models 111  
        Ordinary Least Squares Regression 112  
        Maximum Likelihood Estimates for Linear Models 117  
     Appendix 117  
     Problems 121  
     References 125  
  Poisson Processes 126  
     Basic Definitions 126  
     Properties and Computations 129  
     Extensions of a Poisson Process 132  
        Compound Poisson Processes 132  
        Non-stationary Poisson Process 134  
     Poisson Regression 135  
        Poisson Regression with One Independent Variable 135  
        Poisson Regression with Several Independent Variables 139  
     Appendix 144  
     Problems 147  
     References 150  
  Markov Chains 151  
     Basic Definitions 152  
     Multistep Transitions 155  
     Classification of States 159  
     Steady-State Behavior 167  
     Computations 172  
     Appendix 179  
     Problems 181  
     References 188  
  Markov Processes 190  
     Basic Definitions 190  
     Steady-State Properties 193  
     Revenues and Costs 197  
     Time-Dependent Probabilities 200  
     Appendix 204  
     Problems 205  
  Queueing Processes 209  
     Basic Definitions and Notation 209  
     Single Server Systems 211  
        Infinite Capacity Single-Server Systems 211  
        Finite Capacity Single Server Systems 218  
     Multiple Server Queues 221  
     Approximations 225  
     Appendix 227  
     Problems 228  
     References 233  
  Queueing Networks 234  
     Jackson Networks 234  
        Open Jackson Networks 235  
        Closed Jackson Networks 239  
     Network Approximations 242  
        Deterministic Routing with Poisson Input 243  
        Deterministic Routing with non-Poisson Input 249  
     Appendix 252  
     Problems 253  
     References 256  
  Event-Driven Simulation and Output Analyses 257  
     Event-Driven Simulations 257  
     Statistical Analysis of Output 268  
        Terminating Simulations 269  
        Steady-State Simulations 272  
        Comparing Systems 281  
     Problems 285  
     References 290  
  Inventory Theory 291  
     The News-Vendor Problem 292  
     Single-Period Inventory 295  
        No Setup Costs 295  
        Setup Costs 298  
     Multi-Period Inventory 301  
     Problems 305  
     References 309  
  Replacement Theory 310  
     Age Replacement 310  
        Discrete Life Times 311  
        Continuous Life Times 314  
     Minimal Repair 317  
        Minimal Repairs without Early Replacements 318  
        Minimal Repairs with Early Replacements 319  
     Block Replacement 321  
     Problems 324  
  Markov Decision Processes 327  
     Basic Definitions 328  
        Expected Total Discounted Cost Criterion 330  
        Average Long-Run Cost Criterion 331  
     Stationary Policies 331  
     Discounted Cost Algorithms 333  
        Value Improvement for Discounted Costs 335  
        Policy Improvement for Discounted Costs 336  
        Linear Programming for Discounted Costs 340  
     Average Cost Algorithms 341  
        Policy Improvement for Average Costs 344  
        Linear Programming for Average Costs 348  
     The Optimal Stopping Problem 350  
     Problems 353  
  Advanced Queues 359  
     Difference Equations 360  
     Batch Arrivals 362  
        Quasi-Birth-Death Processes 364  
        Batch Arrivals (continued) 366  
     Phase-Type Distributions 368  
     Systems with Phase-Type Service 372  
        The M/Ph/1 Queueing System 372  
        The M/Ph/c Queueing System 376  
     Systems with Phase-Type Arrivals 378  
     Problems 379  
     References 383  
  Matrix Review 384  
     Matrix Addition and Subtraction 385  
     Matrix Multiplication 385  
     Determinants 386  
     Determinants by Cofactor Expansion 388  
     Nonsingular Matrices 389  
     Inversion-in-Place 390  
     Derivatives 393  
     References 395  
  Index 396  


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