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| Arnold B.C., Balakrishnan N., Nagaraja H.N. — A First Course in Order statistics |
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| Предметный указатель |
 charts 6
Abramowitz, M. 44 82 259
Adaptive estimates 193—194
Admissible matrix 133
Ahmed, S.E. 77 260
Ahsanullah, M. 158 259
Aitken, A.C. 171 259
Allocation of prizes 7
Almost sure convergence 205
Andrews, D.F. 194 259
Annual rainfall 257
Approximations for cumulants 80
Arnold, B.C 119 128 131 133 252 259
Ascending method 95 96
Asymptotic distributions 205—238 244
Asymptotic distributions, joint distributions 219—222
Asymptotic distributions, of central and intermediate order statistics 223—227
Asymptotic distributions, of exponential extremes 207—208
Asymptotic distributions, of extremes from discrete distributions 216—217
Asymptotic distributions, of L statistics 179 227—234
Asymptotic distributions, of maxima and minima 208—216
Asymptotic independence of extremes 221
Balakrishnan, N. 1 37 38 47 59 77 86 87 90 93 99 100—102 105 116—119 128 131 134—136 139 170 173 177 179 180 252 259 260 265 270
Balasubramanian, K. 134 173 260
Balkema, A.A. 225 260
Ballerini, R. 253 260
Barlow, R.E. 39 260
Barnett, V.D 1 103 190 192 194 233 260
Bartholomew, D.J. 170 260
Barton, D.E. 245 262
Basu's Theorem 90 91 93
Basu, D 90 260
Beckman, R.J. 87 90 270
Beg, M.I. 257 265
Bendre, S.M. 116 259
Bennett, C.A. 179 260
Berger, R.L. 2 261
Bernardo, J.M. 82 260
Bernoulli distribution 63—65
Best linear unbiased estimate (BLUE) 159 171—175
Best linear unbiased estimate (BLUE), asymptotic approaches 179—180
Best linear unbiased estimate (BLUE), for exponential distribution 169 176—177
Best linear unbiased estimate (BLUE), for normal distribution 177—179
Best linear unbiased estimate (BLUE), for uniform distribution 168 175 176
Best linear unbiased predictor (BLUP) 160 181 182 199
Beyer, W.H. 44 260
Bhattacharyya, G.K. 167 168 260 266
Bickel, P.J 2 194 259 261
Binomial distribution 59 66—70
Biondini, R 252 261
Birnbaum, A. 38 261
Bishop, Y.M.M. 3 261
Blom, G. 179 261
Boes, D.C 2 267
Bondesson, L. 174 261
Borgan, O. 168 261
Bose, R.C 88 261
Burr, I.W 59 261
Burrows, P.M. 37 261
Cadwell, J.H. 135 261
Cantelli's inequality 247
Casella, G. 2 261
Castillo, E. 1 207 261
Cauchy distribution 103 163 193 237
Cauchy equation 152 158
Cauchy-Schwarz inequality 120 121 122 123 124 125 250
Censored sampling 4 159 178 179
Censoring, progressive 162
Censoring, random 161
Censoring, Type I 160 167 169
Censoring, Type II 161 167 168 174 181 195 197 199 203
Central limit theorem 205 247
Central order statistics 206 223—226
Chan, P.S. 139 173 260
Chandler, K.N. 241 261
Chandrasekar, C 190 267
Characterizations 7 141—158 188
Characterizations, based on moments of order statistics 143—152
Characterizations, geometric distribution 60
Characterizations, involving dependency assumptions 153—155
Characterizations, involving samples of random size 155—157
Chernoff, H. 179 230 261
Chibisov, D.M. 206 261
Clark, C.E. 131 261
Cohen, A.C 1 37 38 90 170 177 179 180 260 261
Complete families of polynomials 144
Complete sufficient statistic 90 91 93 164 188
Computer simulation 95—97
Computing checks 118 135
Conditional distribution of Order statistics 23—26
confidence intervals 162 164 183—185 200 202
Convergence in distribution 205
Convergency in probability 205
Craig, A.T 2 10 164 264
Cramer-Rao inequality 165
Cross-cumulants 131
Culling 6
Cumulant generating function 82
Cumulants 131
D'Agostino, R.B. 187 189 262
Daniell, P.J. 206 230 262
David, F.N. 80 128 131 245 262
David, H.A. xv 1 40 90 119 120 127 128 131 138 185 202 222 262 264
Davis, C.S. 94 262
Davis, H.T. 82 262
Davis, R.C 163 164 262
De Haan, L. 206 209 212 225 260 262
Decreasing failure rate (DFR) 38 39 59
Decreasing failure rate average (DFRA) 39
DeFinetti theorem 251
Delta method 3
Dependent sequences 251
Descending method 95 96
Desu, M.M. 146 262
Devroye, L. 97 262
Discard-deviation 230
Discordant observations 189
Discrete order statistics 41—61 216—217
Discrete order statistics, dependence structure 48—50
Discrete order statistics, geometric distribution 51—53
Discrete order statistics, joint probability mass function 45—48
Discrete order statistics, range 50—51
Discrete order statistics, sampling without replacement 53—56
Discrete Pareto distribution 217
Discrete uniform distribution 43 51 55 58
Distribution free intervals 183—186
Doksum, K.A. 2 261
Domain of attraction 208 211 213
Double-exponential distribution 104
Downton, F. 132 262
Dudewicz, E.J. 2 262
Dudman, J. 38 261
Empirical c.d.f. 187 189
Empirical quantile function 7
Epstein, B. 188 262
Euler's constant 246
Exceedance 236
Exchangeable random variables 54 138 251 252
Exponential distribution, asymptotic distribution of extremes 207—208 215 235
Exponential distribution, best linear unbiased estimates 176 177 196—198
Exponential distribution, censored sample 168 169
Exponential distribution, characterizations 7 141 146—148 150—155 158
Exponential distribution, distribution of order statistics 11 34 35 36 40 72—78 103
Exponential distribution, goodness-of-fit 187—189 201
Exponential distribution, information in an order statistic 165 166
Exponential distribution, likelihood ratio test 188 203
Exponential distribution, outliers 202
Exponential distribution, prediction of order statistics 181 182
Exponential distribution, record values 243—244
Exponential distribution, simulation 95 96
| Exponential distribution, spacings 11 106
Exponential distribution, truncated 97—99
Extreme order statistics 3
Extreme order statistics, asymptotic distribution 3 206—222
Extreme order statistics, moments 44
Extreme order statistics, outliers 190
Extreme order statistics, robust estimation 192
Extreme order statistics, sufficiency 163—64
Extreme processes 241
Extreme value distribution 138 210
Extreme value theory 207
Falk, M 227 263
Feller, W. 245 263
Ferentinos, K.K. 195 263
Ferguson, T.S. 154 263
Fienberg, S.E. 3 261
Fisher information 159 164 166 167 169
Fisher, R.A 3 206 209 216 263
Folded distribution 137
Frechet type 210
Frechet, M. 206 209 263
Galambos, J. 1 142 153 206 209 211 217 219 263
Gamma distribution 38 103 139 174 235
Gamma function 15
Gastwirth, J.L. 179 230 261
Generalized extreme value distribution 210
Generalized quasi-range 32
Generalized record values 241
Gentle, J.E. 97 265
Geometric distribution, constant failure rate 59 60
Geometric distribution, integer part of exponential variable 77
Geometric distribution, minimum and range 51—53 61 153
Geometric distribution, records 254
Geometric distribution, regression 154 155
Geometric distribution, samples of geometric size 156 157
Geometric distribution, spacings 59
George, E.O. 150 263
Gibbons, J.D. 189 263
Gini's mean difference 229—230 238
Glick, N. 242 263
Gnanadesikan, R. 186 187 270
Gnedenko, B. 3 206 211 263
Godwin, H.J. 90 263
Goodness-of-fit 7 141 186—189
Govindarajulu, Z. 93 116 133 135 137 138 263
Graphical procedures 186—187
Graybill, F.A 2 175 263 267
Grechanovsky, E. 13 268
Greenberg, B.G. xv 1 92 168 176—178 198 199 268 269
Grubbs, F.E. 190 191 201 263
Grudzien, Z. 256 263
Gumbel, E.J. 120 206 264
Gupta, A K. 180 264
Gupta, S.S. 38 68 69 82 86 88 100 139 189 261 264
Half logistic distribution 104—106
Hall, P. 216 264
Halperin, M. 168 264
Hamming, R.W. 246 264
Hampel, F.R 194 259
Harter, H.L. 1 87 128 264
Hartley, H.O. 95 96 104 120 264 266
Hawkins, D.M. 192 264
Hochberg, Y. 189 264
Hoeffding, W. 143 264
Hogg, R.V. 2 10 164 193 230 264
Holland, P.W. 3 261
Horn, P.S 96 104 265
Houchens, R.L. 249 265
Huang, J.S. 36 145 265
Huber, P.J 194 259 265
Hundred-year flood 5
Huzurbazar, V.S. 163 265
Improving populations 7 241 252—254
Incomplete beta function 13 30
Incomplete tournaments 7
Increasing failure rate (IFR) 38 39 59 256
Increasing failure rate average (IFRA) 39
Increasing populations 7
Independent spacings 153 155
Inequality measurement 6
Information Inequality 165
Integer part 77
Integrated Cauchy equation 152
Intermediate Order statistics 206 226—227
Internal studentization 102
Interrecord time 242 248 253
Inverse distribution function 2 109
Johns, M.V., Jr. 179 230 261
Johnson, N.L. 80 128 131 262
Johnson, R.A. 167 266
Joint density of n order statistics 10
Joint density of records 244
Joint distribution of two order statistics 16—21 219
Joint normality 226
Joint probability mass function of discrete order statistics 45—48
Joshi, P.C 73 93 97—99 102 103 113 119 134 136 138 260 262 265
Junkins, D.B. 98 268
k-out-of-n system 5
Kabir, A B.M.L. 158 259
Kagan, A M. 142 265
Kahaner, D.K. 87 90 270
Kale, B.K. 202 265
Kaminsky, K.S. 182 265
Kennedy, W.J. 97 265
Khatri, C.G. 203 265
Kipnis, V. 13 268
Kirmani, S.N.U.A 257 265
Kochar, S.C 256 265
Kocherlakota, S. 101 260
Kologorov-Smirnov test 142
Korwar, R.M. 254 265
Kotz, S. 142 153 263
Krishnaiah, P.R. 133 266
Kth record value 256
Kuczma, M. 149 266
L statistics 171 193 206 227—234
Lack of memory 7 243
Lai, T.L. 252 266
Laplace distribution 104 163 193 225 239
Largest order statistic 12 95
Laurent, A.G. 196 266
Law of Large Numbers 205 247
Lawless, J.F. 162 168 183 200 266
Leadbetter, M.R. 206 236 266
Least squares estimates 180
Lehmann, E.L. 163 266
Lewis, T. 1 190 192 194 233 260
Liapounov's conditions 234 247
Lieblein, J. 37 266
Life testing 160
Likelihood ratio test 188 190 203
Likes, J. 182 266
Lindgren, G. 206 236 266
Linear estimates 171—180
Linear regression 155
Lingappaiah, G.S. 200 266
Linnik, Yu.V. 142 265
Lipschitz condition 229
Lloyd, E.H. 159 171 266
Location estimates 4 171—180 194
Log-logistic distribution 156
Log-normal distribution 187
Logistic distribution 37 81—87 96 100 101 150 156 157 230
Logistic order statistics, means and covariances 86 87
Lorenz curve 6
Lower record 220 255
Ludwig, O. 121 122 266
Lurie, D. 95 96 104 266
Malik, H.J. 77 86 87 116 118 134 135 259 260
Malmquist, S. 80 266
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