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Lam Y. — Geometric Process and Its Applications
Lam Y. — Geometric Process and Its Applications

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Название: Geometric Process and Its Applications

Автор: Lam Y.

Аннотация:

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.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 299

Добавлена в каталог: 14.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\delta$-shock      193
$\epsilon$ backward induction outcome      283
$\epsilon$-optimal strategy      279
Adjusted mean squared error (ADMSE)      144
Age      17 42
Appendix      286—289
Asymptotic relative effciency      117
Availability      230
Backward induction outcome      282
Bessel equality      68
Blackwell’s theorem      16
Bounded linear operator      67
Busy period      259
Cauchy — Schwarz inequality      65
Chi-square distribution      116
Classical model for M/M/1 queueing system (classical M/M/1 model)      259
CN strategy      275
Cold standby system      239
Complete orthonormal basis      68
Compound Poisson process      6 191
Compound Poisson random variable      6
Conjugate space      67
Conservative      31
Convolution      11 259
Counting process      2
Cox — Lewis model      8
Cramer $\delta$ theorem      108
CYCLE      18
Decreasing failure rate (DFR)      20
Difference-sign test      104
Directly Riemann integrable      16
Doob decomposition      27
Doob decomposition for GP      40
Dynamic game of complete and perfect information      277
Earlier preventive repair better than later in expectation (ERBLE)      24
Earlier preventive repair worse than later in expectation (ERWLE)      24
Elementary renewal theorem      15
Embedding theorem      73
Equilibrium availability      231
Exponential distribution      4
Extensive form representation of the warranty game      277
Failure rate function      21
Failure repair      23
Free repair (replacement) warranty (FRW)      274
Gamma distribution      6
Geometric distribution      5
Geometric equation      57
Geometric function      55
Geometric process (GP)      37
GP $\delta$-shock model      193
GP model for M/M/1 queueing system with a repairable service station (GP M/M/1 model)      255
GP preventive maintenance model      211
GP shock model      183
GP warranty model      274
Harmonic mean      175
Hilbert space      64
Idle period      262
Increasing failure rate (IFR)      20
Independent and identically distributed (i.i.d.)      5
Independent increments      1
Infinitesimal matrix      31
Inner product      63
Intensity function      7
k-renewal strategy      275
Key renewal theorem      16
Kolmogorov forward equations      51 230
Krickeberg decomposition      29
Krickeberg decomposition for GP      40
Kronecker delta      70
Laplace test      108
Laplace transform      11
Laplace — Stieltjes transform      259
Lattice      11
Least squares estimator      105
Lindeberg condition      107
Lindeberg-Feller theorem      107
Markov chain      31
Martingale      26
Martingale convergence theorem      27
Maximum likelihood estimator (MLE)      113
Maximum percentage error (MPE)      125
Mean squared error (MSE)      125
Mean time to the first failure (MTTFF)      231
Memoryless property      4
Modified GP model (MGP)      126
Moment estimator      105
New better than used in expectation (NBUE)      22
New worse than used in expectation (NWUE)      22
Nonhomogeneous Poisson process      7
Norm      64
Number of thresholds      41
Poisson process      2
Preventive repair      23
Pro-rata warranty (PRW)      274
Rate of occurrence of failures (ROCOF)      31 231
ratio      37
Rational player      278
Regression equation      105
Reliability      231
Renewal equation      10
Renewal function      9
Renewal process      8
Renewal reward process      17
Reproducing kernel function      64
Residual life      17 42
Riesz decomposition      28
Riesz decomposition for GP      40
Shock      182
Slutsky theorem      110
Sojourn time      32
Stationary increments      2
Stochastically increasing      18
Stochastically larger (less)      18
Stopping time      13
Submartingale      26
Supermartingale      26
Supplementary variable      228
Survival function      7
Tauberian theorem      12
Threshold      193
Threshold geometric process (threshold GP)      41
thresholds      41
Total life      17 42
Trapezoidal integration rule      81
Turning point      144
Turning point test      104
Two-component parallel system      234
Two-component series system      227
Waiting time in the queue      268
Waiting time in the system      270
Wald’s equation      14
Wald’s equation for GP      45
Warranty game      276
Weibull process model      8
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