Random Number Generation and Monte Carlo Methods

by James E. Gentle

Subject Index

  • acceptance/complement method, for random number generation 55
  • acceptance/rejection method, for random number generation 45
  • {\sl ACM Transactions on Mathematical Software} 138, 154
  • {\sl ACM Transactions on Modeling and Computer Simulation} 154
  • adaptive direction sampling 66
  • add-with-carry random number generator 26
  • additive congruential random number generator 5
  • alias method, for random number generation 59
  • alias-urn method, for random number generation 61
  • almost exact inversion, for random number generation 50
  • American National Standards Institute, {\it see} ANSI
  • AMS MR classification system 154
  • antithetic variates 14, 117
  • {\sl Applied Statistics} 138, 154, 156
  • AWC random number generator 26
  • ball, generating random points in a ball 93
  • batch means for variance estimation 115
  • Bernoulli distribution, generating random deviates 45, 96
  • beta distribution, generating random deviates 81
  • beta-binomial distribution, generating random deviates 84, 97
  • Beyer ratio 125
  • binary matrix rank test 127
  • binary random variables, generating random deviates 45, 96
  • binomial distribution, generating random deviates 84
  • birthday spacing test 127
  • bit stripping 5, 6, 15
  • bitstream test 127
  • blocks, simulation experiments 34
  • Burr distribution, generating random deviates 88
  • Burr family of distributions 95
  • C (programming language) 137
  • {\sl CALGO} 154, 156
  • Cauchy distribution, generating random deviates 86
  • censored data, simulating 108
  • chi-squared distribution, generating random deviates 81, 83
  • common variates 118
  • {\sl Communications in Statistics -- Series B} 154
  • COMPSTAT 153, 154
  • {\sl Computational Statistics and Data Analysis} 154
  • {\sl Computational Statistics} 154
  • {\sl Computing Science and Statistics} 155
  • congruential random number generator 5
  • constrained sampling 119
  • correlated random variables, generation 53, 98, 106
  • correlation matrices, generating random ones 90
  • craps test 129
  • crude Monte Carlo 112
  • cryptography 2, 3, 27
  • {\sl Current Index to Statistics} 154
  • cycle length of random number generator 3, 6, 15, 16
  • data-based random number generation 99, 141
  • DIEHARD tests for random number generators 126
  • Dirichlet distribution, generating random deviates 94
  • discrepancy 22, 27, 126, 131
  • discrete uniform distribution, generating random deviates 42
  • DNA test for random numbers 128
  • double exponential distribution, generating random deviates 78
  • economical method, for random number generation 56
  • Erlang distribution, generating random deviates 80
  • exact-approximation method, for random number generation 50
  • exponential distribution, generating random deviates 77
  • exponential power distribution, generating random deviates 78
  • Faure sequence 131
  • feedback shift register generator 28
  • Fibonacci random number generator 24
  • folded distribution 73
  • Fortran 90
  • gamma distribution, bivariate extension 95
  • gamma distribution, generating random deviates 79
  • GAMS (Guide to Available Mathematical Software) 138, 156
  • GAMS, electronic access 156
  • Gaussian distribution, {\it see} normal distribution
  • generalized lambda family of distributions, generating random deviates 87
  • geometric distribution, generating random deviates 85
  • geometric splitting 118
  • GFSR (method) 28
  • Gibbs method 66
  • GIS (geographic information system) 105
  • Gray code 133, 134
  • {\sl Guide to Available Mathematical Software}, {\it see} GAMS
  • Halton sequence 131
  • Hastings method 64
  • heat bath method 47
  • heavy-tailed distribution 88
  • hit-and-run method 65, 89
  • hit-or-miss Monte Carlo 47, 112, 118, 121
  • {\tt html} 156
  • hypergeometric distribution, generating random deviates 85
  • importance sampling 118, 121
  • IMSL Libraries 138, 139
  • infinitely divisible distribution, generating random deviates from 67
  • Interface Symposium 153, 155
  • International Association of Statistical Computing (IASC) 153, 154
  • International Standards Organization, {\it see} ISO
  • Internet 155, 156
  • inversive congruential generator 26
  • Java (software system) 156
  • Johnson family of distributions 87
  • {\sl Journal of Computational and Graphical Statistics} 154
  • {\sl Journal of Statistical Computation and Simulation} 155
  • $k$-$d$-tree 100
  • Kepler conjecture 101
  • lagged Fibonacci generator 24
  • lambda family of distributions, generating random deviates 87
  • Laplace distribution, generating random deviates 78
  • Latin hypercube sampling 119
  • lattice test for random number generators 12, 16, 124
  • leapfrogging, in random number generation 13
  • Lehmer congruential random number generator 5
  • Lehmer sequence 5
  • Lehmer tree 34
  • linear congruential random number generator 5
  • log-concave distribution 67
  • logarithmic distribution, generating random deviates 86
  • lognormal distribution, generating random deviates 86
  • majorizing density 46, 95
  • Markov chain Monte Carlo 66
  • {\sl Mathematical Reviews} 154
  • Matlab (software) 138
  • matrix congruential generator 23
  • MCMC (Markov chain Monte Carlo) 66
  • Metropolis-Hastings method 64
  • minimum distance test 128
  • Minkowski reduced basis 125
  • modular arithmetic 3
  • Monte Carlo evaluation of an integral 111
  • Monte Carlo experimentation 147
  • Monte Carlo study 147
  • Mosaic 156
  • MR classification system 154
  • multinomial distribution, generating random deviates 90
  • multiple recursive random number generator 23, 24
  • multiplicative congruential random number generator 5
  • multiply-with-carry random number generator 26
  • multivariate distributions, generating random deviates 89, 99
  • multivariate normal distribution, generating random deviates 89
  • multivariate stable distribution, generating random deviates 95
  • nearest neighbors 100
  • negative binomial distribution, generating random deviates 85
  • {\tt netlib} 138, 154, 156
  • Niederreiter sequence 131, 134
  • noncentral Wishart distribution, generating random observations from 91
  • nonlinear congruential generator 27
  • norm, function 112
  • normal distribution, generating random deviates 74
  • one-way function 2
  • order statistics, generating random 106
  • orthogonal matrices, generating random ones 92
  • over-dispersion 97
  • overlapping pairs test 127
  • overlapping permutation test 127
  • overlapping quadruples test 128
  • overlapping sums test 129
  • parallel processing 31, 33
  • parallel random number generation 33
  • Pareto distribution, generating random deviates 86
  • Pareto-type distribution 88
  • parking lot test 128
  • Pascal distribution, generating random deviates 85
  • patchwork method, for random number generation 48
  • Pearson family of distributions 95
  • period of random number generator 3, 6, 15, 16, 105
  • permutation, generating random ones 103
  • Poisson distribution, generating random deviates 84
  • Poisson process, generating a random one 78
  • Poisson sampling 103
  • primitive polynomial 28, 132
  • probabilistic error bound 112
  • {\sl Proceedings of the Statistical Computing Section} 155
  • projection pursuit 12
  • quasi Monte Carlo method 131
  • quasirandom sequence 131
  • Raleigh distribution, generating random deviates 86
  • random number generator, congruential 5
  • random number generator, feedback shift method 28
  • random number generator, parallel 33
  • random number generator, testing 126
  • random sampling 103
  • {\tt RANDU} 12, 36
  • {\tt rand} 33, 139
  • ratio-of-uniforms method, for random number generation 57, 79, 82
  • rectangle/wedge/tail method, for random number generation 75, 78
  • renewal, simulation experiments 34
  • reproducible research 148
  • reservoir sampling 104
  • residue 4
  • robust statistics 88
  • roughness of a function 112
  • runs test 129
  • S, S-Plus (software) 138, 142
  • sampling, random 103
  • shuffled random number generator 15, 21
  • {\sl SIAM Journal on Scientific Computing} 155
  • side effect 139
  • simulation 147
  • smoothed acceptance/rejection method, for random number generation 118
  • smoothing parameter 99
  • smoothing 99
  • Sobol' sequence 131, 132, 134
  • software engineering 139
  • spectral test for random number generators 12, 16, 124
  • sphere, generating random points on a sphere 92
  • squeeze test 129
  • squeeze, in acceptance/rejection 48
  • stable distribution, generating random deviates 89, 95
  • standard distribution 73
  • Statistical Computing Section of the American Statistical Association 153, 155
  • {\sl Statistics and Computing} 155
  • {\tt statlib} 138, 154, 156
  • stratified sampling 118
  • Student's $t$ distribution, generating random deviates 82
  • subtract-with-borrow random number generator 26
  • SWC random number generator 26
  • swindle, Monte Carlo 116
  • $T$-concave distribution 67
  • table, generating random tables with fixed marginals 93
  • table-lookup method, for random number generation 42
  • Tausworthe random number generator 28
  • testing random number generators 126
  • thinning method 108
  • 3-D sphere test 128
  • transformed density rejection method, for random number generation 67
  • transformed rejection method, for random number generation 49
  • truncated normal distribution 77
  • twisted GSFR generator 31
  • under-dispersion 97
  • uniform time algorithm 72
  • unpredictable 3, 27
  • URL 156
  • urn method, for random number generation 42, 61
  • van der Corput sequence 131
  • variance estimation 115
  • variance reduction 14, 116
  • variance-covariance matrices, generating random ones 90
  • von Mises distribution, generating random deviates 87
  • Web browser 156
  • Weibull distribution, generating random deviates 83
  • weight window 118
  • Wichmann/Hill random number generator 25
  • Wishart distribution, generating random observations from 90
  • World Wide Web (WWW) 156
  • {\tt Xnetlib} 156
  • zeta distribution, generating random deviates 87
  • ziggurat method, for random number generation 76