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| Devroye L. — Generation of non-uniform random variates |
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| Предметный указатель |
2-3 tree 613
2-3 tree in discrete event simulation 747
Abramowitz, M. 297 302 391 415 678
Absolute continuity 172
Absolute value transformation 147
Absorbing Markov chain 757
Acceptance complement method for discrete distributions 116
Acceptance-complement method 75
Acceptance-complement method accelerated 78
Acceptance-complement method for Cauchy distribution 81 451
Acceptance-complement method for Poisson distribution 502
Acceptance-complement method for t distribution 446
Acceptance-complement method of Ahrens and Dieter 77 79
Acceptance-complement method squeeze principle for 78
Aceptance-complement method for nearly flat densities 79
Adaptive inversion method 38
Adaptive strip method 367
Adjacency list 669
Admissible algorithm 9
Admissible generator 9 10
Aflfl, A.A. 606
Aho, A.V. 90 92 214 372 669
Ahrens — Dieter generator for exponential distribution 397
Ahrens, J.H. 36 72 76 77 84 98 121 145 359 379 380 383 391 396 397 405 413 420 423 424 425 432 502 507 518 523 538 617
Aitchison, J. 594
Akima, H. 763
Alder, B.J. 372
Algorithm 2
Algorithm B2PE for beta distribution 305 309
Algorithm B4PE for beta distribution 305
Algorithm of Nijenhuis and Wilf for classical sampling 618
Ali, M.M. 578
Alias method algorithm 108
Alias method bit-based 777
Alias method set-up 109
Alias method with two tables 109
Alias-urn method 110
Almost-exact inversion method 133
Almost-exact inversion method for exponential distribution 134
Almost-exact inversion method for gamma distribution 137 139 141 145
Almost-exact inversion method for monotone densities 134
Almost-exact inversion method for normal distribution 135 380
Almost-exact inversion method for t distribution 143
Alternating series method 153
Alternating series method analysis of 154
Alternating series method exponential version of 154
Alternating series method for exponential distribution 158
Alternating series method for Kolmogorov — Smirnov distribution 162
Alternating series method for Raab — Green distribution 158
Analytic characteristic function 685
Ananthanarayanan, K. 359
Anderson — Darling statistic 168
Anderson, T.W. 168 716
Andrews, D.F. 326
Approximations for inverse of normal distribution function 36
Arc sine distribution 429 481
Arc sine distribution as the projection of a radially symmetric random vector 230
Arc sine distribution deconvolution method 239
Arc sine distribution polar method for 482
Arc sine distribution properties of 482
Archer, N.P. 687
Arfwedson, G. 497
Arfwedson’s distribution 497
Arnason, A.N. 432
Arnold, B.C. 482 583
Arnold, D.B. 592 656
Asau, Y. 96
Assessment of generators 8
Association 574 576 589
Asymmetric Kolmogorov — Smirnov statistics 167
Asymmetric mixtures 71
Asymptotic independence 760
Atkinson — Whittaker method for beta distribution 440 443
Atkinson, A.C. 121 379 380 404 432 439 440 443 480 502 505 507 518
Atkinson’s algorithm for Poisson distribution 518
Autocorrelation matrix 571
AVL tree in discrete event simulation 747
Avoidance problems 372
Avoidance problems grid method for 373
Baase, S. 214
Babu, A.J.G. 304 305 309 432
Badel, M. 571
Bailey, B.J.R. 36
Balanced binary search tree in discrete event simulation 746
Balanced parentheses 652
Ball-in-urn method 608 609
Ball-in-urn method for multinomial distribution 558
Ball-in-urn method for random bipartite graphs 671
Banks, J. 4 736
Barbu, G. 204
Barlow, R.E. 260 277 343 356 742
Barnard, D.R. 367
Barndorff-Nielsen, O. 329 330 478 483
Barnett, V 582
Barr, D.R. 566
Bartels, R. 458 459 460 462
Bartels’s bounds 460 461
Bartlett, M.S. 762
Bartlett’s kernel 762 765 767
Bartlett’s kernel inversion method for 767
Bartlett’s kernel order statistics method for 766
Bartlett’s kernel rejection method for 765
Barton, D.E. 168 519
Basu, D. 594
Batch method for exponential distribution 223
Beasley, J.D. 36
Beckman, R.J. 175
Bell, J.R. 236 380
Bendel, R.B. 606
Bene, B. 4
Bentley, J.L. 215
Berenson, M.X. 215 220
Bergstrom — Feller series for stable distribution 459 460 461
Bergstrom, H. 459 460
Berman, M.B. 416 420
Berman’s method analysis of 419
Berman’s method for beta distribution 418
Berman’s method for gamma distribution 419 420
Berman’s theorem 416
Bernoulli distribution 486 521
Bernoulli distribution properties of 689
Bernoulli generator 769
Bernoulli number 490 493 550
Bernoulli trial 521
Berry — Esseen theorem application of 225
Besag, J.E. 372
Bessel function 469
Bessel function distribution 469
Bessel function distribution type I 469
Bessel function distribution type II 469
Bessel function integral representation for 470
Bessel function modified 469
Bessel function of the first kind 473 755
Bessel function of the second kind 469
Best, D.J. 379 380 405 407 410 420 426 436 447 450 473 474 476
Best’s rejection method for gamma distribution 410
Beta distribution 428
Beta distribution algorithm B2PE for 305 309
Beta distribution algorithm B4PE for 305
Beta distribution algorithm BA for 438
Beta distribution algorithm BB for 438
Beta distribution algorithm BC for 439
Beta distribution as an IHR distribution 343
Beta distribution Atkinson — Whittaker method for 440 443
Beta distribution Berman’s method for 418
Beta distribution Cheng’s rejection method for 438
Beta distribution definition 7
Beta distribution Forsythe’s method for 432
Beta distribution inversion-rejection method for 339 347
Beta distribution Johnk’s method for 418 432 439
| Beta distribution log-concavity of 287
Beta distribution of second kind 25
Beta distribution of the second kind 428 429 437 444
Beta distribution properties of 416 428 429
Beta distribution rejection method for 432
Beta distribution relation to binomial distribution 536
Beta distribution relation to Cauchy distribution 429
Beta distribution relation to Dirichlet distribution 595
Beta distribution relation to F distribution 429
Beta distribution relation to gamma distribution 429 432 595
Beta distribution relation to multivariate Pearson II distribution 237
Beta distribution relation to multivariate Pearson VII distribution 238
Beta distribution relation to order statistics 17
Beta distribution relation to Pearson VI distribution 429
Beta distribution relation to Snedecor distribution 429
Beta distribution relation to t distribution 429
Beta distribution relation to uniform distribution on unit sphere 227
Beta distribution relation to uniform order statistics 210 431
Beta distribution relation to z distribution 330
Beta distribution shape of 428
Beta distribution strip method for 432
Beta distribution uniform order statistics method for 431
Beta distribution universal method for 432
Beta distribution with one or two parameters less than one 439
Beyer, W.H. 245
Bhagavan, B.K. 571
Bhattacharjee, G.P. 678
Bhattacharyya, B.C. 482
Bignami, A. 74
Binary search tree 89 613
Binary search tree in discrete event simulation 747 748
Binary search tree inorder traversal of 89
Binary search tree nearly optimal 94
Binary search tree set-up of 90
Binary tree equivalent 652
Binary tree inorder traversal of 653
Binary tree representation of 652
Binary tree similar 652
Binet’s series 491 497
Binet’s series for the log-gamma function 491
Binomial distribution 486 496 520
Binomial distribution coin flip method for 524
Binomial distribution convergence to normal distribution 526
Binomial distribution definition 84
Binomial distribution first waiting time method for 525
Binomial distribution first waiting time property 522
Binomial distribution generating function of 521
Binomial distribution genesis 521
Binomial distribution inequalities for 527 544
Binomial distribution inversion method for 524
Binomial distribution properties of 497 521 526
Binomial distribution recursive method for 523 536 537 545
Binomial distribution rejection method for 115 523 526 529 533 543
Binomial distribution relation to beta distribution 536
Binomial distribution relation to geometric distribution 522
Binomial distribution relation to hypergeometric distribution 545
Binomial distribution relation to Poisson distribution 543
Binomial distribution second waiting time method for 525
Binomial distribution second waiting time property 522
Binomial distribution sequential search method for 89
Binomial distribution splitting algorithm for 527
Binomial distribution table method for 523
Binomial distribution universal rejection method for 495
Bipartite graph 671
Birth and death process 755
Bisection method 32 38
Bisection method analysis 38
Bit vector 613
Bivariate dependence 576
Bivariate distributions transformations of 577
Bivariate exponential distribution 583 584
Bivariate exponential distribution of Johnson and Tenenbein 585 591
Bivariate exponential distribution of Lawrance and Lewis 585
Bivariate exponential distribution of Marshall and Olkin 585
Bivariate exponential distribution of Moran 585
Bivariate exponential distribution trivariate reduction for 592
Bivariate extreme value distribution 563
Bivariate gamma distribution 586
Bivariate gamma distribution composition method for 587
Bivariate gamma distribution trivariate reduction for 587 588
Bivariate geometric distribution trivariate reduction for 592
Bivariate Hermite distribution 592
Bivariate multinormal distribution 566
Bivariate normal distribution 581
Bivariate Poisson distribution 592
Bivariate Poisson distribution trivariate reduction for 592
Bivariate uniform distribution 576 578 589
Bivariate Weibull distribution trivariate reduction for 592
Black box method 286
Black box method for characteristic function 696
Black box method for log-concave densities 290
Blaesild, P. 478
Blum, M. 431
Bolshev, L.N. 25 136 144 518
Bondesson, L. 458
Boole’s rule 701
Bootstrap estimate 766
Borel — Tanner distribution 520
Boswell, M.T. 4 759
Bounded densities 43
Bounded densities grid method for 376
Bounded densities inversion-rejection method for 332
Bounded densities rejection method for 43
Bounded densities strip method for 360
Bounded monotone densities inversion-rejection method for 345
Box — Muller method for normal distribution 235
Box, G.E.P. 206 235 380
Boyett, J.M. 608
Bratley, P. 4 29 251 736 767
Bray, T.A. 359 380 383 388 392 397
Brent, R. 295
Brent, R.P. 121 380
Brown, G.W. 457
Bryson, M.C. 603 604
Bucket searching 215 218
Bucket sorting 215 219
Bucket sorting analysis of 216 224
Bucket structure 613
Bucket structure in discrete event simulation 743 744 745
Burr distribution 476 477
Burr distribution inversion method for 477
Burr family 476 477 685
Burr XII distribution 423 432 437
Burr XII distribution generator for 411
Burr, I.W. 476
Busy period of a queue 755
Butcher, J.C. 391
Butler, E.X. 763
Cacoullos, T. 446 452
Cacoullos’s theorem 452
Cannon, L.E. 106
Cantelli’s inequality 33
Car parking problem 372
Car parking problem search tree for 374
Carleman’s condition 684
Carlton, A.G. 24
Carson, J.S. 4 736
Catalan’s constant 120
Cauchy distribution 445 450
Cauchy distribution acceptance-complement method for 81 451
Cauchy distribution as a normal scale mixture 326
Cauchy distribution as a stable distribution 183 455
Cauchy distribution as dominating distribution 45
Cauchy distribution closure under addition 25
Cauchy distribution definition 7
Cauchy distribution inversion method for 29 450
Cauchy distribution Kronmal — Peterson generator for 82
Cauchy distribution polar method for 451
Cauchy distribution properties of 452
Cauchy distribution ratio-of-uniforms method for 201
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