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| Devroye L. — Generation of non-uniform random variates |
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| Предметный указатель |
Smirnov, N.V. 161 168
Smith, R.L. 215 220 568
Smoothing parameter 762
Snedecor distribution 429
Sobel, M.J. 749 755
Soni, R.P. 470 756
Sorensen, M. 329 330
Sorting 214
Sowey, E.R. 4
Spacings method for sequential sampling 621
Spacings method for uniform distribution on hypersphere 242
Spearman’s rho 574
Speed 8
Splitting algorithm for binomial distribution 527
Splitting algorithm for monotone densities 335
Springer, M.D. 11 25 469 562 685
Springer, S.G. 36
Square root method 565
Square root transformations 13
Squeeze method 54
Squeeze method analysis of 65
Squeeze method application of 57
Squeeze method for normal distribution 56
Squeeze method for symmetric beta distribution 64
Squeeze method for uniform distribution in unit circle 233
Squeeze principle 53
Squeeze principle application of 141
Squeeze principle for strip method 360
Srinivasan, R. 469
Stable distribution 454
Stable distribution closure under additions 455
Stable distribution convergence to 468
Stable distribution generator of Chambers, Mallows and Stuck for 185 459
Stable distribution inequalities for 461 463
Stable distribution integral representation for 185 459
Stable distribution inversion method for 458
Stable distribution Kanter’s method for 183 459
Stable distribution Levy’s representation for 454
Stable distribution polar representation for 455
Stable distribution properties of 183 184 185 455 456 457
Stable distribution representation for 183
Stable distribution with exponent 1/2 150
Stacy, E.W. 423
Stacy’s generalized gamma distribution 423
Stacy’s generalized gamma distribution rejection method for 423
Stacy’s generalized gamma distribution relation to gamma distribution 423
Stadlober, E. 10 77 446
Standard sequential sampling 619 620
Standish, T.A. 741 747
Steffensen, J.F. 338
Steffensen’s inequality 338
Stegun, I.A. 297 302 391 415 678
Steutel, F.W. 329
Stieltjes’s counterexample 694
Stirling number 658 660
Stirling number of the second kind 658
Stirling number recurrence for 659
Stirling’s series 490
Stoller, D.S. 566
Stopping time 50
Strip method 359
Strip method adaptive 367
Strip method analysis of 361 363
Strip method for beta distribution 432
Strip method for bounded densities 360
Strip method for gamma distribution 406
Strip method for Lipschitz densities 366
Strip method for monotone densities 362
Strip method for Riemann integrable densities 362
Strong, H.R. 104
Stuart, A. 182 420 423 596 678 691 694
Stuart’s theorem 182 420 423 596
Stuck, B.W. 184 185 459
Subbotin, M.T. 175
Suboptimal DDG tree algorithm 775
Sukhatme, P.V. 211
Sum of independent random variables 19 708 714 716
Sum of independent random variables convergence to stable law 734
Sum of independent random variables mixture method for 731
Sum of independent random variables naive method for 717
Sum of independent random variables simulation of 496
Sum of independent uniform random variables 21
Sum of uniform random variables 732
Sum of uniform random variables uniformly fast method for 735
Sum-of-uniforms method 204
Sup correlation 574
Survila, P. 720
Swapping method 612
Swapping method for random permutation 646
Symmetric beta distribution 193 433
Symmetric beta distribution analysis of 433
Symmetric beta distribution convergence to normal distribution 433
Symmetric beta distribution generators for 63 65
Symmetric beta distribution inequalities for 434 441 442
Symmetric beta distribution polar method for 437
Symmetric beta distribution rejection from normal density for 193
Symmetric beta distribution rejection method for 60 434
Symmetric beta distribution relation to t distribution 436 446
Symmetric beta distribution squeeze method for 64
Symmetric beta distribution Ulrich’s polar method for 437
Symmetric binomial distribution 538
Symmetric binomial distribution inequalities for 540
Symmetric binomial distribution rejection method for 539
Symmetric stable distribution 186 455
Symmetric stable distribution as a normal scale mixture 326
Symmetric stable distribution generator for 188
Symmetric stable distribution properties of 189
Symmetric stable distribution series method for 465 466 467
t distribution 10 445
t distribution acceptance-complement method for 446
t distribution almost-exact inversion method for 143
t distribution as a normal scale mixture 326
t distribution composition-rejection method for 446 453
t distribution convergence to normal distribution 447
t distribution discrete 497
t distribution inequalities for 203 447 448 453 454
t distribution inversion method for 445
t distribution properties 15
t distribution ratio-of-uniforms method for 200 204 446
t distribution rejection method for 446 447 450
t distribution relation to beta distribution 429
t distribution relation to F distribution 446
t distribution relation to gamma distribution 427 445 452
t distribution relation to multivariate Cauchy distribution 555
t distribution relation to symmetric beta distribution 436 446
t distribution table method for 446
t distribution with three degrees of freedom 37
t distribution with two degrees of freedom 407 408 429
t3 distribution 446
t3 distribution ratio-of-uniforms method for 202 449
Table look-up 102
Table look-up method 102
Table look-up method Marsaglia’s 106
Table look-up multilevel 106
Table method for binomial distribution 523
Table method for normal distribution 380
Table method for t distribution 446
Tadikamalla, P.R. 215 404 405 420 423 445 477 483 518
Tail of extreme value distribution inversion method for 276
Tail of log-concave densities 308
Tail of Rayleigh distribution inversion method for 29
Tail of the Cauchy distribution 453
Tail of the Cauchy distribution inversion method for 453
Tail of the Cauchy distribution rejection method for 453
Tail of the gamma density 420
Tail of the gamma density rejection method for 421 422 425
Tail of the normal distribution 681
Tail of the normal distribution Marsaglia’s method for 381
Tail of the normal distribution properties of 391
Takahasi, K. 558 600 602
| Talacko, J. 287 471 472
Talbot, D.R.S. 372
Tamarkin, J.D. 682 685 686
Tanner, J.C. 520
Tanner, M.A. 607
Tapia, R.A. 763
Tarjan, R.E. 431
Tashiro, Y. 232
Taylor’s series 55
Taylor’s series for characteristic function 684
Taylor’s series for densities 698
Taylor’s series for logarithm 508
Taylor’s series for normal distribution 384
Teicher, H. 5 21 50 63 225
Teichroew, D. 391
Teichroew’s distribution 391
Tenenbein, A. 576 582 583 585 586 590 591
Teuhola, J. 617
Thinning method 264
Thinning method analysis of 264 266
Thinning method for discrete distributions 280
Thinning method for gamma distribution 277
Thinning method for Poisson processes 253 255
Thisted, R.A. 607
Thompson, J.R. 763
Tietjen, J.L. 175
Time series 571
Tinhofer, G. 657 669 670
Tinhofer’s graph generators 669
Tinhofer’s random graph generator 670
Titchmarsh, E.C. 550
Tiwari, R.C. 594
Toranzos, F.I. 482
Toranzos’s system 482
Transformation of a homogeneous Poisson process 257
Transformation of beta random variables 444
Transformations of random variables 11
Transition matrix 758
Translation parameter 7
Trapezoidal method for normal distribution 383 391
Trapezoidal rule 701
triangle 569
Triangular density 22 23
Triangular density inversion method for 29
Triangulation 570
Trie 104
Trigamma distribution 553
Trivariate reduction 587
Trivariate reduction for bivariate exponential distribution 592
Trivariate reduction for bivariate gamma distribution 587 588
Trivariate reduction for bivariate geometric distribution 592
Trivariate reduction for bivariate Poisson distribution 592
Trivariate reduction for bivariate Weibull distribution 592
Trivedi, K.S. 246
Trojanowski, A.E. 657
Truncated distributions 38
Truncated exponential distribution 401
Truncated extreme value distribution as an IHR distribution 343
Truncated gamma distribution rejection method for 166
Tsang, W.W. 359
Tucker, A.C. 91
Tukey, J.W. 136 457 482
Tukey’s lambda distribution 482
Tukey’s lambda distribution convergence to exponential distribution 483
Tukey’s lambda distribution convergence to logistic distribution 483
Tukey’s lambda distribution generalization of 482 483
Tukey’s lambda distribution properties of 483
Two-way contingency table 608
Ullman, J.D. 90 92 214 372 669
Ulrich, E.G. 571 747
Ulrich, G. 436
Ulrich’s polar method for symmetric beta distribution 437
Uniform distribution 732
Uniform distribution as a beta distribution 428
Uniform distribution as an NBUE distribution 742
Uniform distribution as the projection of a radially symmetric random vector 230
Uniform distribution characteristic function of 708
Uniform distribution definition 7
Uniform distribution distribution of midrange 24
Uniform distribution distribution of products 24
Uniform distribution distribution of ratio of maxima 26
Uniform distribution distribution of sum 21
Uniform distribution in and on circle 233
Uniform distribution in hyperellipsoid 567
Uniform distribution in simplex 568
Uniform distribution in triangle 569
Uniform distribution in unit circle 556
Uniform distribution in unit circle properties of 234
Uniform distribution in unit circle rejection method for 233
Uniform distribution in unit circle relation to Cauchy distribution 234
Uniform distribution in unit circle squeeze method for 233
Uniform distribution mixtures of 16
Uniform distribution on 3d hypersphere generator for 241
Uniform distribution on 4d hypersphere generator for 241
Uniform distribution on a compact set 368
Uniform distribution on a convex set 371
Uniform distribution on a star 243
Uniform distribution on convex polytope 568
Uniform distribution on hypersphere incremental method for 243
Uniform distribution on hypersphere normal random vector method for 230
Uniform distribution on hypersphere properties of 227
Uniform distribution on hypersphere rejection method for 231
Uniform distribution on hypersphere spacings method for 242
Uniform distribution on hypersphere uniform spacings method for 231
Uniform distribution on unit circle efficient rejection method for 235
Uniform distribution properties 25
Uniform distribution sum of independent random variables 144
Uniform line density 572
Uniform order statistics 636
Uniform order statistics exponential spacings method for 214
Uniform order statistics method for beta distribution 431
Uniform order statistics relation to beta distribution 431
Uniform order statistics sorting method for 214
Uniform Poisson process on unit circle 250
Uniform scale mixture 687 688
Uniform spacings 207
Uniform spacings method for 214
Uniform spacings method for exponential distribution 394
Uniform spacings method for uniform distribution on hypersphere 231
Uniform spacings method for uniform order statistics 214
Uniform spacings properties of 208 210 212
Uniform spacings relation to Dirichlet distribution 593
Uniform spacings relation to exponential distribution 208
Uniform sum 732
Uniform sum density of 732 733
Unimodal density grid method for 377
Unimodal distribution 172 687 707
Unimodal distribution inequalities for 173 494
Unimodal distribution matched moment generator for 691
Unimodal distribution rectangular decomposition of 734
Unimodal distribution universal rejection method for 495
Unit sphere volume of 226
Universal generator a la Letac 65
Universal method 286
Universal method for beta distribution 432
Universal rejection method analysis of 317
Universal rejection method for binomial distribution 495
Universal rejection method for convex densities 313
Universal rejection method for discrete distribution 497
Universal rejection method for generalized gaussian distribution 324
Universal rejection method for hypergeometric distribution 545
Universal rejection method for Lipschitz densities 323
Universal rejection method for log-concave densities 301 325
Universal rejection method for monotone densities 312 316 317
Universal rejection method for residual life density 330
Universal rejection method for unimodal distribution 495
Vaduva, I. 47 130 404 415 419 420 424
Vaduva’s gamma generator 130 424
Vaduva’s gamma generator analysis of 131
Vaduva’s rejection method 48
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