Random Number Generation and Monte Carlo Methods, Second Edition

by James E. Gentle

Subject Index

  • acceptance/complement method, for random number generation 106
  • acceptance/rejection method, for random number generation 95, 194
  • {\sl ACM Transactions on Mathematical Software} 240, 288, 292
  • {\sl ACM Transactions on Modeling and Computer Simulation} 288
  • ACORN congruential generator 37
  • adaptive direction sampling 134
  • adaptive rejection sampling 127
  • add-with-carry random number generator 29
  • additive congruential random number generator 8
  • alias method, for random number generation 112
  • alias-urn method, for random number generation 115
  • almost exact inversion, for random number generation 102
  • alternating conditional sampling 133
  • AMS MR classification system 288
  • analysis of variance 203
  • Anderson-Darling test 61
  • antithetic variates 19, 208
  • {\sl Applied Statistics} 240, 288, 291
  • ArcView (software) 293
  • ARMA model 194
  • ARS (adaptive rejection sampling) 127
  • AWC random number generator 29
  • ball, generating random points in 173
  • batch means for variance estimation 202
  • Bernoulli distribution, generating random deviates 88, 174
  • Bernoulli sampling 185
  • beta distribution, generating random deviates 155
  • beta function 279
  • beta-binomial distribution, generating random deviates 159, 175
  • Beyer ratio 56
  • binary matrix rank test 64
  • binary random variables, generating random deviates 88, 174
  • binomial distribution, generating random deviates 159
  • birthday spacing test 64
  • bit stripping 8, 9, 21
  • bitstream test 65
  • blocks, simulation experiments 44
  • Blum/Blum/Shub random number generator 31
  • Boltzmann distribution 219
  • bootstrap, nonparametric 214
  • bootstrap, parametric 215
  • Buffon needle problem 234
  • BUGS (software) 217
  • Burr distribution, generating random deviates 165
  • Burr family of distributions 179
  • C (programming language) 239
  • {\sl CALGO} ({\sl Collected Algorithms of the ACM}) 288, 291
  • cartesian product 274
  • Cauchy distribution, generating random deviates 163
  • CDF (cumulative distribution function) 271
  • cellular automata 36
  • censored data, simulating 191
  • chaotic systems 37
  • Chebyshev generator 38
  • chi distribution, generating random deviates 157
  • chi-squared distribution, generating random deviates 152, 156
  • chi-squared test 60
  • chop down method 92, 162
  • cluster algorithm 220
  • {\sl Collected Algorithms of the ACM} ({\sl CALGO}) 288, 291
  • common variates 209
  • {\sl Communications in Statistics --- Simulation and Computation} 289
  • COMPSTAT 287, 289
  • {\sl Computational Statistics \& Data Analysis} 289
  • {\sl Computational Statistics} 289
  • {\sl Computing Science and Statistics} 289
  • congruential random number generator 8
  • constrained sampling 210
  • control variate 208
  • correlated random variables, generation 104, 180, 189
  • correlation matrices, generating random ones 169
  • craps test 66
  • cross product 274
  • crude Monte Carlo 199
  • cryptography 3, 31, 290
  • cumulative distribution function 271
  • {\sl Current Index to Statistics} 288
  • cycle length of random number generator 2, 9, 21
  • $D$-distribution 155
  • $d$-variate uniformity 53
  • data augmentation 132
  • data-based random number generation 181, 244
  • DIEHARD tests for random number generators 63, 246
  • Dirac delta function 275
  • direct product 274
  • Dirichlet distribution, generating random deviates 176
  • discrepancy 30, 42, 56, 77
  • discrete uniform distribution 185
  • discrete uniform distribution, generating random deviates 89
  • DNA test for random numbers 65
  • double exponential distribution, generating random deviates 150, 178
  • ECDF (empirical cumulative distribution function) 60, 271
  • economical method, for random number generation 107
  • eigenvalues, generating ones from random Wishart matrices 172
  • elliptically contoured distribution 168, 178, 179
  • empirical cumulative distribution function 60, 271
  • empirical test 57
  • entropy 52
  • envelope 95
  • Erlang distribution, generating random deviates 152
  • exact sampling of Markov chain stationary distribution 125
  • exact-approximation method, for random number generation 102
  • Exponent Graphics (software) 293
  • exponential distribution, generating random deviates 149
  • exponential power distribution, generating random deviates 150
  • extended gamma processes 155
  • Faure sequence 78, 79
  • feedback shift register generator 31
  • Fibonacci random number generator 27
  • fixed-point representation 7
  • folded distributions 143
  • Fortran 90 239
  • Galois field 7, 32
  • gamma distribution, bivariate extension 178
  • gamma distribution, generating random deviates 150, 178
  • gamma function 278
  • GAMS ({\sl Guide to Available Mathematical Software}) 241, 292
  • GAMS, electronic access 292
  • generalized gamma distributions 155, 166
  • generalized lambda family of distributions, generating random deviates 165
  • geometric distribution, generating random deviates 160
  • geometric splitting 205
  • GFSR (method) 31
  • Gibbs distribution 219
  • Gibbs method 125, 131, 217
  • GIS (geographic information system) 187
  • GNU Scientific Library (GSL) 240
  • goodness-of-fit test 59, 61
  • Google (Web search engine) 292
  • Gray code 80, 81
  • GSL (GNU Scientific Library) 240
  • halfnormal distribution, generating random deviates 148
  • Halton sequence 78
  • Hamming weight 10
  • Hastings method 120
  • HAVEGE 4
  • Heaviside function 275
  • heavy-tailed distribution 166
  • hit-and-run method 133, 167
  • hit-or-miss Monte Carlo 97, 103, 199, 207, 232
  • hotbits 2
  • {\tt html} 291
  • hypergeometric distribution, generating random deviates 161
  • importance sampling 205, 232
  • importance-weighted resampling 125
  • IMSL Libraries 240, 243, 293
  • incomplete gamma function 279
  • independence sampler 122
  • independent streams of random numbers 44
  • indicator function 275
  • infinitely divisible distribution, generating random deviates from 126
  • instrumental density 95
  • Interface Symposium 287, 289
  • International Association of Statistical Computing (IASC) 287, 289
  • Internet 290, 291
  • inverse CDF method 86
  • inverse CDF method for truncated distributions 142
  • inverse chi-squared distribution 142
  • ``inverse'' distribution 142
  • inverse gamma distribution 142
  • inverse Gaussian distribution, generating random deviates 164
  • inverse Wishart distribution 142
  • inversive congruential generator 29
  • Ising model 218
  • iterative method, random number generation 117, 131
  • Java (programming language) 291
  • Johnson family of distributions 165
  • {\sl Journal of Computational and Graphical Statistics} 289
  • {\sl Journal of Statistical Computation and Simulation} 289
  • $k$-$d$-tree 182
  • Kepler conjecture 184
  • Kolmogorov distance 61
  • Kolmogorov-Smirnov test 60, 61
  • lagged Fibonacci generator 27
  • Lahiri's sampling method 194
  • lambda family of distributions, generating random deviates 165
  • Landau distribution 167
  • Lapace distribution, generating random deviates 178
  • Laplace distribution, generating random deviates 150
  • Laplacian operator 277
  • Latin hypercube sampling 210
  • lattice test for random number generators 16, 17, 55
  • leaped Halton sequence 79
  • leapfrogging, in random number generation 19, 36, 46
  • Lehmer congruential random number generator 8
  • Lehmer sequence 8
  • Lehmer tree 44
  • linear congruential random number generator 8
  • Lisp-Stat (software) 293
  • log-concave distributions 127
  • logarithmic distribution, generating random deviates 162
  • lognormal distribution, generating random deviates 148
  • Lorentzian distribution, generating random deviates 163
  • M(RT)$^2$ algorithm 220
  • majorizing density 95, 174
  • Maple (software) 293
  • Markov chain 117
  • Markov chain Monte Carlo 122, 125, 131, 216, 217
  • Markov process 192
  • Mathematica (software) 293
  • {\sl Mathematical Reviews} 288
  • {\tt mathml} 291
  • Matlab (software) 240, 293
  • matrix congruential generator 28
  • MCMC (Markov chain Monte Carlo) 122, 125, 131, 216, 217
  • Mersenne prime 9
  • Mersenne twister 35
  • Metropolis algorithm 220
  • Metropolis-Hastings method 120, 131, 217
  • ``minimal standard'' generator 10, 17, 23, 51, 69
  • minimum distance test 66
  • Minkowski reduced basis 55
  • mixture distributions 94
  • modular arithmetic 6
  • Monte Carlo evaluation of an integral 198
  • Monte Carlo experimentation 253
  • Monte Carlo study 253
  • Monte Carlo test 212
  • Mosaic (Web browser software) 291
  • MR classification system 288
  • MT19937 (generator) 35
  • multinomial distribution, generating random deviates 169
  • multiple recursive random number generator 26, 29
  • multiplicative congruential random number generator 8
  • multiply-with-carry random number generator 29
  • multivariate distributions, generating random deviates 167, 181
  • multivariate double exponential distribution, generating random deviates 178
  • multivariate gamma distribution, generating random deviates 178
  • multivariate hypergeometric distribution, generating random deviates 177
  • multivariate Laplace distribution, generating random deviates 178
  • multivariate normal distribution, generating random deviates 168
  • multivariate stable distribution, generating random deviates 178
  • nearest neighbors 182
  • negative binomial distribution, generating random deviates 160
  • {\tt netlib} ix, vi, 240, 288, 291
  • Niederreiter sequence 78, 81
  • NIST Test Suite, for random number generators 67
  • noncentral hypergeometric distribution, generating random deviates 161
  • noncentral Wishart distribution, generating random observations from 170
  • nonhomogeneous Poisson process 193
  • nonlinear congruential generator 30
  • nonparametric bootstrap 214
  • norm, function 199
  • normal distribution, generating random deviates 144
  • one-way function 3
  • order statistics, generating random 189
  • orthogonal matrices, generating random ones 171
  • over-dispersion 175
  • overlapping pairs test 65
  • overlapping permutation test 64
  • overlapping quadruples test 65
  • overlapping sums test 66
  • parallel processing 36, 44, 46
  • parallel random number generation 44
  • parametric bootstrap 215
  • Pareto distribution, generating random deviates 163
  • Pareto-type distribution 166
  • parking lot test 66
  • Pascal distribution, generating random deviates 160
  • patchwork method, for random number generation 99
  • Pearson family of distributions 165, 179
  • period of random number generator 2, 9, 21, 188
  • permutation, generating random ones 185
  • $\pi$ as a source of random numbers 36
  • Poisson distribution, generating random deviates 160
  • Poisson process, generating a random one 149
  • Poisson process, nonhomogeneous 193
  • Poisson sampling 186
  • portability of software 38, 39, 86, 103, 141
  • Potts model 221
  • primitive polynomial 32, 79
  • primitive root 10
  • probabilistic error bound 200
  • {\sl Proceedings of the Statistical Computing Section} 289
  • projection pursuit 16
  • PV-Wave (software) 293
  • quasi-Monte Carlo method 77
  • quasirandom sequence 4, 77
  • R (software) 240, 246, 293
  • R250 (generator) 34
  • random number generator, congruential 8
  • random number generator, feedback shift method 31
  • random number generator, parallel 44
  • random number generator, testing 57
  • random sampling 185
  • {\tt RANDU} 16, 47, 69
  • {\tt rand} 39, 241
  • ratio-of-uniforms method, for random number generation 109, 151, 157
  • Rayleigh distribution, generating random deviates 163
  • rectangle/wedge/tail method, for random number generation 146, 149
  • renewal, simulation experiments 44
  • reproducible research 254
  • resampling 213
  • reservoir sampling 186
  • residue 6
  • robust statistics 166
  • roughness of a function 199
  • runs test 61, 67
  • S, S-Plus (software) 240, 246, 293
  • sampling, random 185
  • sampling/importance resampling 125
  • second-order test 63
  • seed 8, 18, 19, 45, 242, 245, 248
  • sequential importance sampling 207
  • setup time 139
  • shuffled random number generator 21, 40
  • {\sl SIAM Journal on Scientific Computing} 289
  • side effect 241
  • simple random sampling 185
  • simplex 182
  • simulated annealing 117
  • simulation 1, 123, 253
  • SIR (sampling/importance resampling) 125
  • skew-normal distribution 143
  • skewed distribution 143
  • smoothed acceptance/rejection method, for random number generation 207
  • smoothing parameter 181
  • smoothing 181
  • Sobol' sequence 78, 79, 81
  • software engineering 241
  • spanning trees, generating random ones 187
  • spectral test for random number generators 16, 17, 54
  • sphere, generating random points on a sphere 172
  • SPRNG, software for parallel random number generation 46, 251
  • squeeze test 66
  • squeeze, in acceptance/rejection 98
  • stable distribution, generating random deviates 167, 178
  • standard distributions 141
  • Statistical Computing Section of the American Statistical Association 287, 289
  • {\sl Statistical Computing \& Graphics Newsletter} 289
  • {\sl Statistics and Computing} 289
  • {\tt statlib} ix, vi, 240, 289, 291
  • stratified sampling 205
  • Student's $t$ distribution, generating random deviates 157
  • substitution sampling 132
  • subtract-with-borrow random number generator 29
  • Super-Duper (generator) 40
  • SWC random number generator 29
  • Swendsen-Wang algorithm 220
  • swindle, Monte Carlo 204
  • $T$-concave distributions 130, 134
  • table, generating random tables with fixed marginals 173
  • table-lookup method, for random number generation 89
  • Tausworthe random number generator 31
  • testing random number generators 57
  • thinning method 193
  • 3-D sphere test 66
  • transendental numbers as a source of random numbers 36
  • transformed density rejection method, for random number generation 130
  • transformed rejection method, for random number generation 102
  • truncated distributions 141, 142
  • truncated gamma distribution 153, 154
  • truncated normal distribution 148, 169
  • twisted GSFR generator 35
  • twos-complement representation 7
  • under-dispersion 175
  • uniform time algorithm 140
  • universal methods 86
  • unpredictable 3, 31
  • urn method, for random number generation 89, 115
  • van der Corput sequence 78
  • variance estimation 202
  • variance reduction 19, 204
  • variance-covariance matrices, generating random ones 169
  • Vavilov distribution 167
  • von Mises distribution, generating random deviates 164
  • W3C (World Wide Web Consortium) 291
  • Web browser 291
  • Weibull distribution, generating random deviates 158
  • weight window 206
  • weighted resampling 125
  • Wichmann/Hill random number generator 40, 49
  • Wilson-Hilferty approximation 148
  • Wishart distribution, generating random observations from 169
  • Wolff algorithm 220
  • World Wide Web Consortium 291
  • {\tt xml} 291
  • {\tt Xnetlib} 292
  • XploRe (software) 294
  • Yahoo (Web search engine) 292
  • zeta distribution, generating random deviates 163
  • ziggurat method, for random number generation 108, 147
  • Zipf distribution, generating random deviates 164