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| Devroye L. — Generation of non-uniform random variates |
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| Предметный указатель |
Cauchy distribution relation to beta distribution 429
Cauchy distribution relation to gamma distribution 427
Cauchy distribution relation to normal distribution 240 451 452
Cauchy distribution relation to uniform distribution in unit circle 234
Cauchy distribution tail of 453
Cawdery, M.N. 367
Cayley’s Theorem 662
Central limit theorem 21 136 222
Central limit theorem for binomial distribution 526
Central limit theorem local 719
Chalmers, C.P. 606
Chambers, J.M. 184 185 459
Characteristic function 6 19 695
Characteristic function black box method for 696
Characteristic function definition 5
Characteristic function inequalities for 707 721
Characteristic function of uniform distribution 708
Characteristic function Polya 718
Characteristic function rejection method for 697
Characteristic function with compact support 706 712
Chebyshev’s inequality 321
Chen, H.C. 96
Cheng, R.C.H. 194 203 405 406 411 412 413 423 432 437 438 439 477
Cheng’s rejection method for beta distribution 438
Cheng’s rejection method for gamma distribution 411 413 423
Cherian, K.C. 587
Chernin, K.E. 183 184 455 459
Chhikara, R.S. 148
Chi-square distribution 403
Chi-square distribution properties 13
Chmielewski, M.A. 226
Chow, Y.S. 5 21 50 63 225 323
Cinlar, E. 246 251 257 261
Circle avoidance problem 372
Circle parking problem 374
Circular array in discrete event simulation 741
Cislak, P.J. 476
Classical sampling 612
Classical sampling algorithm of Nijenhuis and Wilf for 618
Classical sampling analysis of 614 615
Classical sampling with membership checking 613
Classical sampling with membership checking based on a hash table 616
Closed hashing 613 617
Codeword 662
Coding function 559 643
Coding function for binary tree 657 658
Coding function for edges in a graph 668
Coding function for random partition 661
Cohen, J. 673
Coin flip method for binomial distribution 524
Coin flips simulation of 104
Compact support 43
Comparison-based inversion methods 88
Compiled code 8
Complete binary tree 90
complexity 2
Composition method 66 68
Composition method analysis of 69
Composition method based upon hazard rates 262
Composition method for bivariate gamma distribution 587
Composition method for discrete distributions 116
Composition method for multivariate distributions 557
Composition method for normal distribution 67
Composition method for order statistics 224
Composition method for Poisson processes 253
Composition method for polynomial densities 71 72
Composition method modified 69
Composition method with quick acceptance 263
Composition-rejection method for gamma distribution 420
Composition-rejection method for normal distribution 380 382
Composition-rejection method for t distribution 446 453
Compound Poisson distribution 487
Compound Weibull distribution 414
Comprehensive family 581
Concave distribution 172
Concave monotone densities inequalities for 328
Concave monotone densities universal rejection method for 329
Conditional density 555
Conditional distribution method 555
Conditional distribution method for Gumbel’s bivariate exponential family 584
Conditional distribution method for Morgenstern’s family 580
Conditional distribution method for multinomial distribution 558 559 731
Conditional distribution method for multinormal distribution 556
Conditional distribution method for multivariate Cauchy distribution 555
Conditional distribution method for normal distribution 556
Conditional distribution method for random  table 610
Conditional distribution method tables for 561
Connected graph 668
Consistency 762
Consistent density estimate 762
Context-free language 673
Contingency table 608
Continuous mixtures definition 16
Convergence to the stable distribution 468
Convergent series method 152
Convergent series method analysis of 156
Convex characteristic function 186
Convex densities 179
Convex densities generator for 180
Convex densities inequalities for 311
Convex densities inversion-rejection method for 355
Convex densities universal rejection method for 313
Convex density inequalities for 322
Convex distribution 172
Convex hull 571
Convex polygon in the plane 570
Convex polytope 568
Convolutions 19
Cook — Johnson distribution 600 602
Cook — Johnson distribution properties of 601
Cook, J.M. 241
Cook, R.D. 600 602
Cooper, B.E. 678
Cornish — Fisher approximation 136
Correlated random variates 29
Correlation coefficient 573
Covariance matrix 564
Covariance matrix random vector with given 565
Cox, D.R. 258
Cramer, H. 733
Cumulative hazard rate 260
Cyclic rate function 256
Dagpunar, J.S. 426
Dahl, O.J. 743
Darboux, M. 460 462
Darboux’s formula 460 462
Darling, D.A. 168 716
Davey, D. 743 746
David, F.N. 587
Davidovic, Ju.S. 309
Davis, P.J. 701 704
DDG tree 771
DDG tree algorithm 771
DDG tree algorithm analysis of 772
DDG tree algorithm optimal 777
DDG tree algorithm suboptimal 775
DDG tree for rejection method 777
DDG tree relation to finite state machine 782
de Balbine, G. 648 651
de Matteis, A. 74
Deak, I. 4 77 232 566
Decoding function 559
Decoding method 643
Decoding method for random binary tree 657
Decoding method for random permutation 644
Decoding method Robson’s 648
Decoding with rejection 645
Decomposition of a polytope 570
Deconvolution method 239
Deconvolution method for arc sine distribution 239
| Definition 16
Denardo, E.V. 746
Densities with known moments 324
density 5
Density estimate 759
Density estimate consistency of 762
Density inequalities for 696 698 705
Dependence 573
Depth of a node 649
Derivatives of characteristic function inequalities for 703
Devroye, L. 4 35 49 151 162 167 169 187 216 218 261 264 268 277 278 288 331 334 406 422 502 507 523 544 568 621 624 625 626 675 676 680 696 759 762 763 764 766 767
DHR distributions 261
DHR distributions dynamic thinning method for 268 283
DHR distributions inversion method for 267
DHR distributions inversion-rejection method for 342 344
DHR distributions properties of 277
Diagonal matrix 605
Dice simulation of 103
Dieter, U. 72 76 77 121 145 379 380 383 391 396 397 405 413 420 423 424 425 432 502 507 518 523 538 617
Digamma distribution 553
Diggle, P.J. 372
Dirichlet distribution 593
Dirichlet distribution generalization of 596
Dirichlet distribution relation to beta distribution 595
Dirichlet distribution relation to gamma distribution 594
Dirichlet distribution relation to uniform spacings 593
Dirichlet tessellation 374
Discrete distribution 83
Discrete distribution generating tree 771
Discrete distribution inequalities for 497
Discrete distribution universal rejection method for 497
Discrete dynamic thinning method 283
Discrete event simulation 735
Discrete hazard rate function 278
Discrete Markov chain 757 758
Discrete mixtures 66
Discrete normal distribution rejection method for 117
Discrete random variable 83
Discrete t distribution 497
Discrete thinning method analysis of 282
Discrete thinning method for logarithmic series distribution 282
Discrete thinning method for negative binomial distribution 284
Discrete uniform distribution 88
Distribution function 5
Distribution function inequalities for 321
Distributions on hyperspheres 571
Dubey, S.D. 414
Dudewicz, E.J. 483
Dugue, D. 186
Dumouchel, W.H. 458
Durstenfeld, R. 648
Duval, P. 743 744 746
Dvoretzky, A. 373
Dynamic hashing 38
Dynamic thinning method analysis of 269
Dynamic thinning method for DHR distributions 268
Easton, M.C. 619
Economical method 77
Eigenvalue 605
Empiric distribution function 167
Energy spectrum of fission neutrons 191
Englebrecht-Wiggans, R. 743
entropy 771 775
Equiprobable mixture 106
Erdos — Kac distribution 170
Erdos — Kac distribution series method for 170
Erdos, P. 170 668
Ernvall, J. 617
Error estimates for inversion formula 702
Euler’s constant 424 552 639 680
Evans, J.O. 36
Event simulator 673
Event-driven simulation 736
Expected complexity 2
Experimental method explicit approximations for inverse of distribution function 35
Experimental method for geometric distribution 499
Explicit factorial model 631
Exponential class of distributions 38
Exponential distribution Ahrens — Dieter generator for 397
Exponential distribution almost-exact inversion method for 134
Exponential distribution alternating series method for 158
Exponential distribution as an IHR distribution 343
Exponential distribution batch method for 223
Exponential distribution definition 7
Exponential distribution generating iid random variates 223
Exponential distribution inequalities for 157
Exponential distribution inversion method for 29
Exponential distribution Marsaglia’s generator for 394 396
Exponential distribution memoryless property 212
Exponential distribution memoryless property of 219 393
Exponential distribution mixtures of 16
Exponential distribution Monahan’s algorithm for 132
Exponential distribution order statistics of 219
Exponential distribution properties 12
Exponential distribution properties of 125 393 395
Exponential distribution ratio-of-uniforms method for 200
Exponential distribution rectangle-wedge-tail method for 397
Exponential distribution relation to exponential integral distribution 176
Exponential distribution relation to normal distribution 240
Exponential distribution relation to Poisson process 248
Exponential distribution relation to Weibull distribution 414
Exponential distribution series method for 168
Exponential distribution truncated 157
Exponential distribution uniform spacings method for 394
Exponential distribution von Neumann’s method for 125
Exponential function inequalities for 721
Exponential inequalities 142
Exponential integral distribution properties of 191
Exponential integral distribution relation to exponential distribution 176
Exponential inter-arrival time method for Poisson distribution 504
Exponential mixtures 176
Exponential order statistics 219
Exponential power distribution 174
Exponential power distribution log-concavity of 287
Exponential power distribution multivariate properties of 244
Exponential power distribution rejection method for 302
Exponential power distribution relation to gamma distribution 175 193 420
Exponential scale mixture 329
Exponential spacings 211
Exponential spacings method for exponential order statistics 219
Exponential spacings method for Poisson process 249
Exponential spacings method for uniform order statistics 214
Extendible hashing 104
Extremal value distribution relation to logistic distribution 39
Extreme value distribution bivariate 563
Extreme value distribution log-concavity of 287
Extreme value distribution relation to Weibull distribution 414
F distribution definition 23
F distribution relation to beta distribution 429
F distribution relation to gamma distribution 23 428
F distribution relation to t distribution 446
Factorial moment 486
Factorial moment generating function 486
Factorial representation 644
Factorials evaluation of 489
Faddeeva, V.N. 565
Fagin, R. 104
Fama, E. 458
Fan, C.T. 620 624
Farlie, D.J.G. 578 589
Feast, G.M. 194 203 406
Fejer-de la Vallee Poussin density 187 459 718
Fejer-de la Vallee Poussin density rejection method for 187
Fejer-de la Vallee Poussin distribution 169
Feller, W. 161 168 172 184 246 326 329 452 453 454 455 457 459 460 468 469 470 563 654 684 693 715 721
Ferreri, C. 482
Ferreri’s system 482
Finite mixtures 66
Finite state machine relation to DDG tree 782
First passage time distribution 150
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