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| Devroye L. — Generation of non-uniform random variates |
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| Предметный указатель |
Inversion method for Cauchy distribution 29 450
Inversion method for DHR distributions 267
Inversion method for discrete distributions 85
Inversion method for exponential distribution 29
Inversion method for exponential family of distributions 38
Inversion method for generating the maximum 675
Inversion method for geometric distribution 87 499 500
Inversion method for hyperbolic secant distribution 472
Inversion method for logarithmic series distribution 546
Inversion method for logistic distribution 39 471
Inversion method for maxima 30
Inversion method for multivariate discrete distributions 560
Inversion method for normal distribution 380
Inversion method for order statistics 30
Inversion method for Pareto distribution 29 262
Inversion method for Poisson distribution 502 505
Inversion method for Poisson processes 251 252
Inversion method for power function distribution 262
Inversion method for Rayleigh distribution 29
Inversion method for stable distribution 458
Inversion method for t distribution 445
Inversion method for t3 distribution 37
Inversion method for tail of extreme value distribution 276
Inversion method for tail of Rayleigh distribution 29
Inversion method for tail of the Cauchy distribution 453
Inversion method for triangular density 29
Inversion method for Weibull distribution 262
Inversion method for wrapped Cauchy density 474
Inversion method in sequential sampling 621 624
Inversion method numerical approximation algorithms for 31
Inversion of a many-to-one transformation 146
Inversion-rejection method 331
Inversion-rejection method analysis of 337 342 345 351
Inversion-rejection method for beta distribution 339 347
Inversion-rejection method for bounded densities 332
Inversion-rejection method for bounded monotone densities 345
Inversion-rejection method for convex densities 355
Inversion-rejection method for DHR distributions 342
Inversion-rejection method for IHR distributions 342
Inversion-rejection method for Lipschitz densities 348
Inversion-rejection method for monotone densities 336 341
Inversion-rejection method optimization of 339 347
Inversion-with-correction 625
Inzevitov, P. 720 731
Irving, D.C. 4 480
Jackson-de la Vallee Poussin distribution 169
Jacobian 14
Jacobs, P.A. 571
Jansson, B. 4 648
Jigsaw puzzle method 67
Johnk, M.D. 416 420 432
Johnk’s method analysis of 419
Johnk’s method for beta distribution 418 432 439
Johnk’s method for gamma distribution 418 420
Johnk’s theorem 416
Johnson — Ramberg bivariate uniform family 592
Johnson — Ramberg method for normal distribution 244
Johnson — Ramberg method for radially symmetric distributions 237
Johnson — Tenenbein family 582 583
Johnson — Tenenbein family properties of 590
Johnson — Tietjen — Beckman distribution 175
Johnson — Tietjen — Beckman distribution relation to gamma distribution 175
Johnson, D.G. 606
Johnson, M.E. 175 237 244 404 576 582 583 585 586 587 590 591 592 600 602 603 604
Johnson, M.M. 175
Johnson, NX. 7 84 379 480 484 496 498 552 555 600 602 604 688
Johnson’s family 484
Johnson’s system 484 685
Jonassen, A. 743
Jones, T.G. 620
Jorgensen, B. 287 478
k-excellence 764
Kac, M. 170
Kachitvichyanukul, V. 502 507 523 545
Kadoya, M. 583 590
Kaminsky, F.C. 261
Kanter, M. 183 184 455 459
Kapadia, C.H. 322
Kawarasaki, J. 631
Kawata, T. 731
Keilson, J. 329
Kelker, D. 226 228 326
Kelly, F.P. 372
Kelton, W.D. 4 736
Kemp, A.W. 86 546 547 559 560 593 759
Kemp, C.D. 559 560 561 592 593 759
Kemp’s generator for logarithmic series distribution 548
Kendall, D.G. 547
Kendall, M. 678 691 694
Kendall-Stuart density 694
Kendall’s tau 574
Kennedy, W.J. 4
Kent, J. 329 330
Kernel estimate 687 762
Kernel estimate analysis of 767
Kernel estimate consistency of 767
Kernel estimate in Monte Carlo integration 766
Kernel estimate mixture method for 765
Khinchine’s theorem 172 687
Kimeldorf — Sampson bivariate uniform distribution 589
Kimeldorf, G. 574 575 576 589 590
Kinderman, A.J. 194 195 201 203 379 380 383 390 391 406 446 454
Kinderman-Ramage generator for normal distribution 391
Kingston, J.H. 737 746 747
Klincsek, T. 216 218
Klingsberg, P. 663
Klingsberg’s algorithm 664 665
Knopp, K. 493 498
Knopp’s series 493
Knopp’s series for the log-gamma function 493
Knott, G.D. 657
Knuth, D.E. 4 214 502 618 638 743 747 768 771 774 777 779 781
Knuth-Yao lower bound 772
Kohrt, K.D. 36 84 98 359
Kolmogorov — Smirnov distribution 161
Kolmogorov — Smirnov distribution alternating series method for 162
Kolmogorov — Smirnov distribution series expansions for 161
Kolmogorov — Smirnov statistic 168
Kolmogorov, A.N. 161 168
Korenbljum, B.I. 309
Kotz, S. 7 84 379 469 480 496 498 552 555 600 602 604
Kowalski, C.J. 603
Krein’s condition 684
Kronmal, R.A. 75 81 82 108 110 359 369 451
Kruskal, W.H. 574
Kuiper, N.H. 168
Kuiper’s statistic 168
Kullback, S. 402 423
Labeled free tree 66*5
Laha, R.G. 451 469
Laha’s distribution 451
Lai, R. 426 587 588 591
Lakhan, V.C. 571
Lancaster, H.O. 589
Laplace distribution as a normal scale mixture 326
Laplace distribution as dominating distribution 44
Laplace distribution generators for 119
Laplace distribution properties of 401
Laplace distribution relation to normal distribution 25
Law, A.M. 4 736
Lawrance — Lewis bivariate exponential distribution 585
Lawrance, A.J. 571 583 585 586 591
Lehmer, D.H. 644
Lehmer’s factorial representation 644
Leipnik, R. 694
Leitch, R.A. 458
Lekkerkerker, C.G. 288
Letac, G. 52
Letac’s lower bound 52
Letac’s lower bound application of 124
| Levy, P. 457
Levy’s representation for stable distribution 454
Lewis, P.A.W. 251 253 256 258 259 261 264 571 583 585 586 591
Li, F.S. 136
Li, S.T. 571
Library traversal 561
Lieblein, J. 26
Line distribution 571 572
Linear list back search in 742
Linear list front search in 742
Linear list in discrete event simulation 740
Linear selection algorithm 431
Linear transformations 12 563
Linnik, Yu.V. 186 720
Linnik’s distribution 186
Linnik’s distribution generator for 190
Linnik’s distribution properties of 189
Liouville distribution 596
Liouville distribution generalization of 599
Liouville distribution of the first kind 596
Liouville distribution properties of 598
Liouville distribution relation to Dirichlet distribution 598
Lipschitz condition 63 320
Lipschitz densities inequalities for 320 322
Lipschitz densities inversion-rejection method for 348
Lipschitz densities proportional squeeze method for 63
Lipschitz densities strip method for 366
Lipschitz densities universal rejection method for 323
Littlewood, J.E. 338
Local Central Limit Theorem 719 720
Local central limit theorem application of 58
Local central limit theorem for gamma distribution 404
Loeve, M. 697
Log-concave densities 287
Log-concave densities black box method for 290
Log-concave densities inequalities for 288 290 295 296 299 321 325
Log-concave densities optimal rejection method for 293 294
Log-concave densities properties of 309
Log-concave densities rejection method for 291 292 298 301
Log-concave densities tail inequalities for 308
Log-concave densities universal rejection method for 301 325
Log-concavity of 287
Log-concavity of properties 39
Log-concavity of properties of 472 480
Log-concavity of rejection method for 471
Log-concavity of relation to extremal value distribution 39
Log-concavity of relation to extreme value distribution 472
Logarithm inequalities for 140 168 198 508 540 722
Logarithmic series distribution 488 545
Logarithmic series distribution definition 84
Logarithmic series distribution discrete thinning method for 282
Logarithmic series distribution inversion method for 546
Logarithmic series distribution Kemp’s generator for 548
Logarithmic series distribution properties of 284 546 547
Logarithmic series distribution rejection method for 546 549
Logarithmic series distribution relation to geometric distribution 547
Logarithmic series distribution sequential test method for 282
Logistic distribution 471 518
Logistic distribution as a normal scale mixture 326
Logistic distribution as a z distribution 330
Logistic distribution definition 39
Logistic distribution generators for 119
Logistic distribution inequalities for 471
Logistic distribution inversion method for 39 471
Lognormal distribution 392 484
Lognormal distribution moments of 693
Lost-games distribution 758 759
Lotwick, H.W. 372 374
Loukas, S. 559 560 561 592 593
Lower triangular matrix 564
Lukacs, E. 186 469 694
Lurie, D. 215
Lusk, E.J. 733
Lux, I. 60 176
Lux’s algorithm 61
Lyapunov’s inequality 324
m-ary heap in discrete event simulation 747
M/M/l queue 755 759
Maclaren, M.D. 359 380 397
Maclaurin series 460
Maejima, M. 720 731
Magnus, W. 470 756
Mallows, C.L. 168 184 185 326 459
Malmquist, S. 212
Malmquist’s theorem 212
Maly, K. 746 747
Mandelbrot, B. 454
Mannion, D. 373
Mantel, N. 25
Many-to-one transformations 145
Mardia, K.V. 473 576 581 587 588 589
Mardia’s generator for Plackett’s family 589
Marginal density 555
Marginal distribution 6
Marginal random variable 6
Markov chain transition matrix 758
Markov’s inequality 321
Marsaglia — Bray generator for normal distribution 390 392
Marsaglia, G. 4 53 67 106 133 135 136 137 141 143 144 236 241 242 359 378 380 381 382 383 388 392 394 395 397 406 446 605 606
Marsaglia’s algorithm RGAMA for gamma distribution 406
Marsaglia’s almost-exact inversion method 136
Marsaglia’s approximation 136
Marsaglia’s generator for exponential distribution 394 396
Marsaglia’s method for tail of the normal distribution 381
Marsaglia’s table look-up method 106
Marshall, A.W. 277 343 356 563 576 583 585 774
Mason, R.L. 215
Matched moment generator 690
Matched moment generator for unimodal distribution 691
Matching distribution 519
Matching distribution rejection method for 520
Maximal correlation 29 574 580
Maximum distribution of 19
Maximum inversion method for 30 675
Maximum of a gamma sample 678
Maximum of a normal sample 678
Maximum of a uniform sample 210
Maximum quick elimination algorithm for 676
Maximum record time method for 679 680
Maximum simulation of 674
Maxwell distribution relation to normal distribution 176
Maxwell, W.L. 743
May, J.H. 568
McCallum, D. 112
McCormack, W.M. 737 743 747
McGrath, E.J. 4 480
McKay, A.T. 482
McKay, J.K.S. 661
McMullen, P. 571
Mean value 5
Median 5
Median density of 18
Median of a uniform sample 18
Mergesort 214
Method of guide tables 96 97
Method of guide tables analysis of 97
Method of Lewis and Shedler 264
Method of Michael, Schucany and Haas 146
Method of percentiles 484
Michael, J.R. 145
Mickey, M.R. 606
Mikhail, N.N. 578
Mikhailov, G.A. 176 177 191 571
Mikhailov’s theorem 177
Minimal spacing 213
Minimax strategy 762
Mirror principle 295
Mirror principle for random walk 654
Mirror principle for unimodal densities 329
Mirsky, L. 682
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