Allen A. — Probability, statistics, and queueing theory with computer science applications :: Электронная библиотека попечительского совета мехмата МГУ

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Allen A. — Probability, statistics, and queueing theory with computer science applications

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Название: Probability, statistics, and queueing theory with computer science applications

Автор: Allen A.

Аннотация:

This is a textbook on applied probability and statistics with computer science applications for students at the upper undergraduate level. It may also be used as a self study book for the practicing computer science professional. The successful first edition of this book proved extremely useful to students who need to use probability, statistics and queueing theory to solve problems in other fields, such as engineering, physics, operations research, and management science. The book has also been successfully used for courses in queueing theory for operations research students. This second edition includes a new chapter on regression as well as more than twice as many exercises at the end of each chapter. While the emphasis is the same as in the first edition, this new book makes more extensive use of available personal computer software, such as Minitab and Mathematica.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-nd edition

Год издания: 1990

Количество страниц: 763

Добавлена в каталог: 02.02.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$C^{2}_{X}$       see "Squared coefficient of variation"
$M/H_{2}/1$ queueing system      313—315
$M/M/\infty$ queueing system      284—285
Allen — Cunneen approximation formula      341
Alternative hypothesis      486
Analysis of variance (ANOVA), for multiple linear regression      592—594
Analysis of variance (ANOVA), in simple linear regression      567—570
Analysis of variance (Anova), one-way      534—539
Anderson — Darling $A^{2}$ test      525—533
ANOVA table for multiple linear regression      593
ANOVA table for one way ANOVA      536
ANOVA table for simple linear regression      567
Approximations for queueing systems      see "Queueing theory"
Armstrong, Neil      489
Arrival theorem      391
Axioms of a $\sigma$ -algebra      16
Axioms of a probability measure      see "Probability measures"
Bayes' theorem      29
Benchmark      464
Benchmark, Dhrystones      465—466
Benchmark, Linpack      465
Benchmark, Livermore Loops      465—466
Benchmark, Whetstones      465—466
Bernoulli tests      506—514
Bernoulli tests, one sample      506—510
Bernoulli tests, two sample      510—514
Bernoulli, process      204
Bernoulli, random variables      see "Discrete probability distributions"
Bernoulli, sequence of trials      74
Bernoulli, trial      74 111
Berra, Yogi      449
Bias      435
Binomial coefficient      22
Binomial distribution      111—113
Binomial distribution as approximation to hyper-geometric distribution      182—183
Binomial distribution, normal approximation to      159—162
Binomial distribution, Poisson approximation to      117—119
Binomial random variables      see "Discrete probability distributions"
Birth-and-death process      210—221
Birthday problem      32—34
Blake, William      210
Bonferroni's inequalities      see "Inequalities"
Bortkiewicz      116 120 478 517—518
Bottleneck      380—381
Box-and-whiskers plot      462—464
Boxplot      see "Box-and-whiskers plot"
Bridge (the game)      20 88—90 100—101
Brown, Peter F.      224
Browning, Elizabeth Barrett      20
Buzen's algorithm      390
Caesar, Julius      502
Carroll, Lewis      40 60 429 477
Carter, Jimmy      616
Central limit theorem      158—164
Central server model of multiprogramming      389—400
Chapman — Kolmogorov equations      222
Chebyshev inequality      see "Inequalities"
Chi-square distribution      144—146
Chi-square tests      515—524
Chi-square tests, categories (cells)      515—516
Coefficient of determination, $R^{2}$       571
Coefficient of multiple determination, $R^{2}$       594
Coefficient of multiple determination, $R^{2}$ , adjusted, $R^{2}_{a}$       594
Coefficient of skewness      461
Combination      20 24
Combinatorial analysis      20—24
Complement of event      13
Conditional density function      61—62
Conditional expectation      60—67
Conditional kth moment      62
Conditional probability      24—34
Conditional probability mass function      61
confidence intervals      442—449
Confidence intervals for differences of two means      449 497—503
Confidence intervals for mean ( $\sigma$ known)      443
Confidence intervals for mean ( $\sigma$ unknown)      445
Confidence intervals for mean response in regression      576
Confidence intervals for proportion      447—448
Confidence intervals for regression coefficients      565 595
Confidence intervals for variance      446
Contingency tables      520—524
Continuity correction      160
Continuous probability distributions      121—158
Continuous probability distributions, bivariate normal      135—136
Continuous probability distributions, chi-square distribution      144—146
Continuous probability distributions, Coxian      154—158
Continuous probability distributions, Erlang-k      141—144
Continuous probability distributions, exponential      38—39 43—44 123—129
Continuous probability distributions, F      147—148
Continuous probability distributions, gamma      137—141
Continuous probability distributions, hyperexponential      148—154
Continuous probability distributions, normal      129—135
Continuous probability distributions, Student's t      146—147
Continuous probability distributions, uniform      121—123
Continuous random variables      38—40 121—158
Continuous random variables, jointly      47
Convolution      58
Convolution, algorithm for central server model      389
Convolution, theorem      57
Correlation analysis      557 572—577
Correlation coefficient      51 555 571
Correlation coefficient, sample, r      571—575
Counting process      201—202
Covariance      51
CPU bound      349 380—381
Critical region      487
Cumulative distribution function      see "Distribution function"
Curve fitting      556
Curve of regression      556
Cyclic queueing models      347—349
D/D/c/K/K queueing system (machine repair)      687
Daley's conjecture      339
David, Karl      106 241 615
DeMoivre — Laplace limit theorem      159—160
Density function      38
Density function, joint      47
DFITS      582
Diaconis, Persi      450
Dirac delta function      168
Discrete probability distributions, Bernoulli distribution      73—74 111
Discrete probability distributions, binomial distribution      74 111—113
Discrete probability distributions, geometric distribution      114—115
Discrete probability distributions, hypergeometric distribution      181 441
Discrete probability distributions, multinomial distribution      180
Discrete probability distributions, multivariate hypergeometric distribution      183
Discrete probability distributions, negative binomial (Pascal) distribution      184—185
Discrete probability distributions, Poisson distribution      59 70 115—120 185—186
Discrete probability distributions, uniform      120
Discrete random variables      110—120
Discrete random variables, definition      36 110
Distribution function      35
Distribution function, marginal      46
Donne, John      442
EDA      see "Exploratory data analysis"
EDF tests      524—534
EDF tests, quadratic statistics      525
Ehrenberg, A.S.C.      20
Ehrenfest urn model      233
Einstein, Albert      110 121 502 616
Elementary renewal theorem      238
Emerson, Ralph Waldo      615
Empirical distribution function      524
Empty set, $\emptyset$       12
Equally likely outcomes      15
Ergodic      228—232
Erlang's B formula, B[c,a]      282—283
Erlang's C formula, C[c,a]      275—276
Erlang's delay formula      see "Erlang's C formula"
Erlang's loss formula      see "Erlang's B formula"
Erlang-k random variables      see "Discrete probability distributions"

Error sum of squares      534 564 567
Error, type I      488 490
Error, type II      488 490
Estimation of regression parameters      591—594
Estimators      431—442
Estimators, consistent      433
Estimators, efficient      435
Estimators, maximum likelihood      437—439 441—442 447
Estimators, method of moments      436—437
Estimators, minimum mean-squared error      435
Estimators, minimum variance unbiased      435
Estimators, unbiased      433
Event      10—14
Event, complement of      13
Event, elementary      10
Event, impossible      see "Empty set"
Events, complementary      13
Events, independent      27
Events, mutually exclusive      14
Expected value      40—41 50
Exploratory data analysis, (EDA)      450
Exponential random variables      see "Continuous probability distributions"
F-distributed random variables      147—148
Feller, William      44 81 88 116 138 161 180 227 228 230 420 442
FESC (flow equivalent service center)      406—408
Finite population queueing models      381—386
Finite processor-sharing model of computer system      385—386
Fitted values      566
Forced flow law      379—380
Gambler's ruin      232—233
Gamma function      137
Gamma random variables      see "Continuous probability distributions"
Generating function (z-transform)      72—73
Geometric random variables      see "Discrete probability distributions"
George, David Lloyd      508
GI/M/1 queueing system      315—321
GI/M/c queueing system      321—324
Goldwyn, Samuel      555
Goodness-of-fit tests      515 see "Kolmogorov
Halsey, Admiral William      449
Ham's algorithm      280—281
Ham, Russell      61 95 121 279
Hart, Oliver J.      610
Hat matrix      579
Hawking, Stephen      616
Head-of-the-line system      see "HOL priority queueing system"
Heavy traffic approximation      336
Henry, Patrick      24
histogram      450—458
Hoffenstein, Samuel      486 524
HOL priority queueing system      328
Holmes, Sherlock      1 46 527
Homogeneous in time      220
Hyperexponential random variables      148—154
Hyperexponential random variables, algorithms for generating      149—152
Hypothesis testing      485
Hypothesis testing, test procedure      486—487
I/O bound      380
Impossible event      see "Empty set"
Independent events      see "Events"
Independent increments      203
Independent random variables      49—50
Inequalities      76—85
Inequalities, Bonferroni's inequalities      82
Inequalities, Bonferroni's inequality      82—83
Inequalities, Chebyshev's inequality      77—79
Inequalities, Markov's inequality      76—77
Inequalities, one-sided inequality      79—81
Influential point      578
Interarrival time      254
Interval estimation      576—577
Jackson's theorem      386
Jackson, James R.      386 387
Joint distribution function      52
Joint probability density function      47
Joint probability mass function      46
Kay, Mimi      388
Kelly-Bootle, Stan      67 76 247 377 449 464 508
Kelvin, Lord (William Thomson)      158
Kendall notation      257
Kendall, David      257
Kleinrock, Leonard      306 315 327 337 385 386
Knuth, Donald      94
Kobayashi, Hisashi      296 313
Kolmogorov — Smirnov test      528—533
Kreyszig, Erwin      433 446 490
Kronecker delta function      222
Kruskal — Wallis test      544—546
kurtosis      461—462
Kurtosis, coefficient of      461
Laplace transform      75 164—171 176—177
Laplace — Stieltjes transforms      75—76 164—170 176—177
Law of Large Numbers      84
Law of the unconscious statistician      41
Law of total expectation      63
Law of total moments      63
Law of total probability      26
Least squares, line      563
Least squares, method of      560—569
Life, current      237
Life, excess      237
Life, total      237
Likelihood function      438
Lincoln, Abraham      461
Literary Digest      430
Little's formula      see "Little's law"
Little's Law      259—260
Little's result      see "Little's law"
Little, John D.C.      259 260
Longfellow, Henry Wads worth      14 589
Lutek, Ben W.      106 247 664
M/G/1 priority queueing systems      326—331
M/G/1 processor-sharing queueing system      331—334
M/G/1 queueing system      302—315
M/G/1/K/K queueing system, (machine repair), general repair time      292—296
M/M/1 queueing system      262—269
M/M/1/K queueing system      269—274
M/M/1/K/K queueing system (machine repair)      285—292
M/M/c loss system      see "M/M/c/c queueing system"
M/M/c queueing system      274—281
M/M/c/c queueing system      282—284
M/M/c/K queueing system      284
M/M/c/K/K queueing system (machine repair, multiple repairmen)      297—301
Machine repair queueing system      see "D/D/c/K/K" "M/M/1/K/K" "M/M/c/K/K
Marginal distribution function      46
Marginal probability mass function      46
Markov chains      219—233
Markov chains, aperiodic      224
Markov chains, irreducible      224
Markov chains, periodic      224
Markov inequality      see "Inequalities"
Markov process      219—220
Markov property of exponential distribution      123—124
Markov property of geometric distribution      115
Mass points      36
Maximum Likelihood Estimation      see "Estimation maximum
McCae, Charles      500
Mean      40
Mean value analysis (MVA)      378
Mean value analysis (MVA), algorithm for central server model      390—391
Mean value analysis (MVA), algorithm for closed multiclass model      411
Mean value analysis (MVA), algorithm for mixed multiclass model      415
Mean, arithmetic      431 458 474
Mean, generalized harmonic      469—470 473—474
Mean, geometric      471—474
Mean, harmonic      466—468 474
Mean, sample (also called arithmetic)      431—432 458
Mean, weighted arithmetic      476—477
Mean, weighted geometric      471 476—477
Mean, weighted harmonic      476—477

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