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| Balakrishnan N., Nevzorov V.B. — A Primer on Statistical Distributions |
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| Предметный указатель |
 distribution 281
 distribution 281
 -algebra 1 15
'Student' 240 286 293
Absolutely continuous bivariate distribution 16 18 19 21
Absolutely continuous distribution 2 9
Actuarial analysis 74
Aitchison, J. 234 289
Altmann, G. xv 293
Arcsine distribution 140 149 151—156 186 231
Arcsine distribution, Characteristic function 154
Arcsine distribution, Characterizations 155
Arcsine distribution, Decompositions 156
Arcsine distribution, Introduction 151
Arcsine distribution, Moments 153 154
Arcsine distribution, Notations 151 152
Arcsine distribution, Relationships with other distributions 155
Arcsine distribution, Shape characteristics 154
Arnold, B.C 18 133 289
asymptotic relations 228
Auxiliary function 211
Balakrishnan, N. xv xvi 68 72 157 197 203 289 291 293
Bansal, N. 230 289
Basu, A.P. 157 289
Behboodian, J. 230 289
Bell-shaped curve 140 241
Bernoulli distribution 37 43—50 56 63 69 72 87 98 112 277
Bernoulli distribution, Bernstein's theorem 221—223
Bernoulli distribution, Convolutions 45 46
Bernoulli distribution, Introduction 43
Bernoulli distribution, Maximal values 46 47
Bernoulli distribution, Moments 44 45
Bernoulli distribution, Notations 43 44
Bernoulli distribution, Relationships with other distributions 47 48
Bernoulli, J. 277
Bernoulli, N. 277
Bernstein, S.N. 221 289
Beta distribution 8 59 115 117 139—149 151 152 155 156 186 207 231 245 272—275
Beta distribution of the second kind 140 275
Beta distribution, Characteristic function 147
Beta distribution, Decompositions 148 149
Beta distribution, Introduction 139
Beta distribution, Mode 140
Beta distribution, Moments 141
Beta distribution, Notations 140
Beta distribution, Relationships with other distributions 149
Beta distribution, Shape characteristics 147
Beta distribution, Some transformations 141
beta function 101 102 118 139
Bilateral exponential distribution 170
Binomial distribution 39 46 49—61 63 69 80 83 88 89 94—96 98 99 102 211 219 228 249 252 253 255 277
Binomial distribution, Conditional probabilities 58 59
Binomial distribution, Convolutions 56
Binomial distribution, Decompositions 56 57
Binomial distribution, Generating function and characteristic function 50
Binomial distribution, Introduction 49
Binomial distribution, Maximum probabilities 53
Binomial distribution, Mixtures 57 58
Binomial distribution, Moments 50—53
Binomial distribution, Notations 49
Binomial distribution, Tail probabilities 59
Binomial distribution, Useful representation 50
Binomial expansion 175
Borel cr-algebra 1 15
Borel set 1 15
Box — Muller's transformation 229
Box, G.E.P. 229 289
Brown, J.A.C 234 289
Brownian motion 152
Burr system of distributions 277
Burr, I.W. 277 283 289
Cacoullos, T. 241 289
Castillo, E. 18 289
Cauchy distribution 12 117 119—122 170 230 232 233 236 278
Cauchy distribution, Characteristic function 120
Cauchy distribution, Convolutions 120
Cauchy distribution, Decompositions 121
Cauchy distribution, Moments 120
Cauchy distribution, Notations 119
Cauchy distribution, Stable distributions 121
Cauchy distribution, Transformations 121
Cauchy function 278
Cauchy — Schwarz inequality 8
Cauchy, A.-L. 278
Central limit theorem 228
Characteristic function 10—14 22 23 33 34 37 40 45 46 50 56 60 61 64 74 81 90 96 97 110 111 120 121 125 126 131 132 147 148 154 158 159 170 173 181 185 188 195 201 203—206 209 210 214 216 217 219 222 23 225 230—239 254—263 265 267 278 282
Chhikara, R.S. 238 289
Chi distribution 232 282
Chi-square distribution 180 226 227 231 239 240 245 246 280
Closed under minima 134
Cobb — Douglas distribution 234
Compositions 250
Compound Poisson distribution 98
Comrie, L.J. 283
Conditional distribution 18 20 58 71 83 94 95 99 185—187 219 220 251—253 267 268 273
Conditional expectation 20 21
Conditional mean 20 21 273
conditional probabilities 58 59 72 94 95
Conditional variance 268
Consul, P.C 100 290
Contour integration 120
Convex function 10
Convolution formula 201
Convolutions 34 35 41 45 46 56 68 69 76 92 111 120 164 165 173 185 217—219
Correlation coefficient 19 20 116 252—254 257 259 265 268 274 275
Correlation matrix 19
Countable set 16
Covariance 19 116 164 252 255 259 274
Covariance matrix 19 253 257 259 261 263 265
Cramer's result 222
Cramer, H. 219 290
Crow, E.L. 234 290
Cumulants 216
Darmois — Skitovitch's theorem 224—226
Darmois, D. 224 290
David, F.N. 281
Decompositions 14 35 36 41 56 57 69 70 76 80 92 111 121 148 149 156 165 166 174 185 204 217—219
Degenerate distribution 14 36 39—41 49 214 216 222 223
Degenerate distribution, Convolution 41
Degenerate distribution, Decomposition 41
Degenerate distribution, Independence 40
Degenerate distribution, Introduction 39
Degenerate distribution, Moments 39 40
Degenerate normal distribution 265
Destructive process 99
Determinant 24 260 265
Devroye, L. 237 290
Diagonal matrix 263 264
Differential equation 8 210
Dirichlet distribution 269—276 278
Dirichlet distribution of the second kind 275 276
Dirichlet distribution, Derivation of Dirichlet formula 271 272
Dirichlet distribution, Dirichlet distribution of the second kind 275
Dirichlet distribution, Introduction 269 270
Dirichlet distribution, Liouville distribution 276
Dirichlet distribution, Marginal distributions 272
Dirichlet distribution, Marginal moments 274
Dirichlet distribution, Notations 272
Dirichlet distribution, Product moments 274
Dirichlet integral formula 27—272 274 276 278
Dirichlet, J.P.G.L. 270 272 278 290
Discrete bivariate distribution 16 18—20
Discrete random walk 47
Discrete rectangular distribution 29
Discrete uniform distribution 29—37 43 71 107 117
Discrete uniform distribution, Convolutions 34 35
Discrete uniform distribution, Decompositions 35 36
Discrete uniform distribution, Entropy 36
Discrete uniform distribution, Generating function and characteristic function 33 34
Discrete uniform distribution, Introduction 29
| Discrete uniform distribution, Moments 30—33
Discrete uniform distribution, Notations 29 30
Discrete uniform distribution, Relationships with other distributions 36 37
Double exponential distribution 170 191
Doubly exponential distribution 191
Douglas, J.B. 98 290
Eggenberger, F. 101 290
Elderton, W.P. 281
Elementary events 15
Elliptically symmetric distributions 281
entropy 8 9 36 45 70 110 131 137 162 172 211
Erlang distribution 39
Euclidean space 15
Euler's constant 195
Euler's formula 204
Evans, M. xv 290
Expectation 5 7 50 109
Exponential decay 160
Exponential distribution 39 113 114 117 157—167 169 170 174 175 177 179 180 186 187 189 192 194 229 230 235 236 269 271
Exponential distribution, Convolutions 164 165
Exponential distribution, Decompositions 165 166
Exponential distribution, Distributions of minima 162
Exponential distribution, Entropy 162
Exponential distribution, Introduction 157
Exponential distribution, Lack of memory property 167
Exponential distribution, Laplace transform and characteristic function 158 159
Exponential distribution, Moments 159 160
Exponential distribution, Notations 157 158
Exponential distribution, Shape characteristics 160
Exponential distribution, Uniform and exponential order statistics 163 164
Exponentially decreasing tails 198 199
Extreme value distributions 170 189—197 201 204 206 228
Extreme value distributions, Generalized extreme value distributions 193 194
Extreme value distributions, Introduction 189 190
Extreme value distributions, Limiting distributions of maximal values 190 191
Extreme value distributions, Limiting distributions of minimal values 191
Extreme value distributions, Moments 194—196
Extreme value distributions, Relationships between extreme value distributions 191
Extremes 280
F distribution 245 246 279 285
F test 246
Fang, K.T. 281
Feller, W. 98 290
Fermat's last theorem 278
First law of Laplace 170
Fisher — Snedecor distribution 286
Fisher's distribution 240
Fisher's z-distribution 279
Fisher, R.A. 279 280
Folded distribution 176
Folks, J.L. 238 289
Fourier transform 278
Fractional part 166
Frechet, R.-M. 279 280
Frechet-type distribution 191 279
Fuchs, L. 290
Functional equation 18 190
Galambos, J. 281
Galton, F. 284
Gamma distribution 92 165 179—188 206 207 208 228 231 239 271 272
Gamma distribution, Conditional distributions and independence 185 187
Gamma distribution, Convolutions and decompositions 185
Gamma distribution, Introduction 179
Gamma distribution, Laplace transform and characteristic function 181
Gamma distribution, Limiting distributions 187 188
Gamma distribution, Mode 180
Gamma distribution, Moments 181 182
Gamma distribution, Notations 180
Gamma distribution, Shape characteristics 182
Gamma function 75 179 195 204 270
Gauss — Laplace distribution 211
Gauss, C.F. 279
Gaussian distribution 211
Gaussian law 211
Generalized arcsine distribution 140 155
Generalized extreme value distributions 193 194
Generalized gamma distribution 184
Generalized logistic distributions 205—207
Generalized logistic distributions, Type I 205 206
Generalized logistic distributions, Type II 205 206
Generalized logistic distributions, Type III 206 207
Generalized logistic distributions, Type IV 206 207
Generalized Poisson distribution 98 100
Generalized uniform distribution 114
Generating function 10 11 13 22 24 33 34 36 50 64 68 69 72—74 81 84 90 92 96 98 99 254 255
Geodesy 280
Geometric distribution 39 48 63—75 80 102 166
Geometric distribution, Conditional probabilities 71 72
Geometric distribution, Convolutions 68 69
Geometric distribution, Decompositions 69 70
Geometric distribution, Entropy 70
Geometric distribution, Generating function and characteristic function 64
Geometric distribution, Geometric distribution of order k 72
Geometric distribution, Introduction 63
Geometric distribution, Moments 64—67
Geometric distribution, Notations 63
Geometric distribution, Tail probabilities 64
Gilchrist, W.G. 3 290
Gnedenko, B.V. 280
Godambe, A.V. 98 290
Goodness-of-fit 281
Gosset, W.S. 280 283 290
Govindarajulu, Z. 176 290
Gradshteyn, I.S. 31 290
Gupta, R.D. 270 276 290
Haight, F.A. 89 291
Half logistic distribution 203 204
Hamedani, G.G. 230 289
Hartley, H.O. 283
Hastings, N. xv 290
Heavy-tailed distribution 286
Helmert's transformation 226 227 280
Helmert, F.R. 226 280 291
Hypergeometric distribution 59 71 83—89 102
Hypergeometric distribution, Characteristic function 84
Hypergeometric distribution, Generating function 84
Hypergeometric distribution, Introduction 83
Hypergeometric distribution, Limiting distributions 88
Hypergeometric distribution, Moments 84—87
Hypergeometric distribution, Notations 83 84
Hypergeometric function 33 84 148 154
Identity matrix 264
Incomplete beta function 139
Indecomposable 14 35 36 156
Independent random variables 16 17 21—23 40 128 135 148 152 156 162 166 185—187 220—229 263 264 270
Inferential problems 180 240 241
Infinitely divisible characteristic function 14
Infinitely divisible distribution 14 57 70 80 92 166 174 185 219 233
Integer part 166
Integrated Cauchy functional equation 285
Interarrival times 39
Inverse distribution function 112
Inverse Fourier transform 170 209
Inverse gaussian distribution 237 238
Inverse transformation 24
Jacobian 24 25 186 229 267 269—271 275
Johnson's system of 234 281
Johnson, N.L. xv 98 148 234 278 280 281 283 291
Joint characteristic function 221 222 225
Joint probability density function 17 18 115 116 185—187 226 227 229 270 271
Jones, M.C 242 291
Kagan, A. 282 285
Kemp, A.W. xv 291
Kemp, C.D. 98 291
Kendall, D.G. 39 291
Key, E.S. 230 289
Klugman, S.A. 74 291
Kolmogorov distribution 281
Kolmogorov, A.N. 281 291
Kolmogorov-Smirnov test 281
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