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| Balakrishnan N., Nevzorov V.B. — A Primer on Statistical Distributions |
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| Предметный указатель |
Kotz, S. xv 98 148 169 281 290 291
Koutras, M.V. 72 289
Kozubowski, T.J. 169 291
Krasner, M. 36 291
Kronecker, L. 290
Krysicki, W. 148 156 291
kurtosis 7 8 44 45 52 53 66 76 91 110 125 129 147 154 160 172 182 201 238 241 283
Lack of memory property 71 167
Lagrangian — Poisson distribution 100
Lancaster, H.O. 240 292
Laplace distribution 165 169—177 191 204 214 236 282
Laplace distribution, Characteristic function 170
Laplace distribution, Convolutions 173
Laplace distribution, Decompositions 174
Laplace distribution, Entropy 172
Laplace distribution, Introduction 169
Laplace distribution, Moments 171
Laplace distribution, Notations 169 170
Laplace distribution, Shape characteristics 172
Laplace transform 158 159 164 179 181
Laplace, P.S. 169 282 292
Lattice distribution 29
Lau — Rao characterization theorem 285
Law of Large Numbers 277
Least squares method 211
Leptokurtic distribution 8 53 66 76 91 147 160 172 182 201 238 241
Life-time data analysis 184 196
Light-tailed distribution 286
Limit process 152
Limit theorems 256 257
Limiting distribution 37 39 59—61 81 88 96 182 187—193 209 228 256—259 280 286
Linear combinations 220—228 262 263
Linear dependence 265
Linear regression 268
Linnik distribution 235—237 282
Linnik, Yu.V. 237 282 285 292
Liouville integral formula 276
Liouville, J. 276 292
Location parameter 4 6 30 127 134 158 169 184 190 198 211 216 220 272
Log — Weibull distribution 191
Log-gamma distribution 184 207
Log-logistic distribution 277
Logarithmic distribution 99
Logistic distribution 197—207 277
Logistic distribution, Characteristic function 201
Logistic distribution, Decompositions 204
Logistic distribution, Generalized logistic distributions 205—207
Logistic distribution, Introduction 197
Logistic distribution, Moments 199—201
Logistic distribution, Notations 197 198
Logistic distribution, Order statistics 205
Logistic distribution, Relationships with other distributions 203
Logistic distribution, Shape characteristics 201
Lognormal distribution 233 234 281
Lukacs, E. 186 292
Marcinkiewicz, J. 214 228 292
Marginal distribution function 16—18 21 250—252 266 273
Marsaglia, G. 186 292
Maxima 46 47 113 114 127 128 189—191 193 228 280
Maximal sum 152
Maxwell distribution 232 282
Maxwell, J.C 282
Mean 5 8 30 72 100 103 115 118 153 154 192 203 205 211 216 217 220 233 234 239 241 245 246 255
Mean vector 19 257 261 265
Measurable function 20 21
Mesokurtic distribution 8 53 147
Minima 113 114 134 162 189—191 286
Mixture distribution 57 58 96—99
Moment generating function 12 184
Moments 4 7 8 12 30—33 39 40 44 45 50—53 64—67 74—76 84—87 90 91 108—110 118 120 124 125 129 136 137 141—146 153—155 159 160 171 174 175 181 182 184 186 194—196 199—201 206 215 216 228 234 237 241 245 252—254
Moments about p 125
Moments about zero 4—6 30 44 50 52 65 75 87 91 108 124 129 136 145 153 155 159 171 181 199 200 215 216
Moments of negative order 146 181
Moments, central 5 6 8 30 44 50 52 66 76 91 109 124 125 136 137 145 153 155 160 171 182 200 216
Moments, Factorial 6 7 10 30 31 51 64 65 74 75 86 90
Moments, Marginal 274
Moments, Product 19 176 274
Moments, Second-order 260 261
Monte Carlo evaluation 286
Muller, M.E. 229 289
Multinomial distribution 249—257 259
Multinomial distribution, Compositions 250
Multinomial distribution, Conditional distributions 251 252
Multinomial distribution, Generating function and characteristic function 254 255
Multinomial distribution, Introduction 249
Multinomial distribution, Limit theorems 256 257
Multinomial distribution, Marginal distributions 250 251
Multinomial distribution, Moments 252—254
Multinomial distribution, Notations 250
Multinomial trials 249—251
Multiple regression 254
Multivariate normal distribution 257 259—268
Multivariate normal distribution, Bivariate normal distribution 265—268
Multivariate normal distribution, Distributions of sums 262
Multivariate normal distribution, Independence of components 263
Multivariate normal distribution, Introduction 259 260
Multivariate normal distribution, Linear combinations of components 262 263
Multivariate normal distribution, Linear transformations 264 265
Multivariate normal distribution, Marginal distributions 262
Multivariate normal distribution, Notations 260 261
Negative binomial distribution 69 70 73—81 89 102 209 228
Negative binomial distribution, Convolutions and decompositions 76—80
Negative binomial distribution, Generating function and characteristic function 74
Negative binomial distribution, Introduction 73 74
Negative binomial distribution, Limiting distributions 81
Negative binomial distribution, Moments 74—76
Negative binomial distribution, Notations 74
Negative binomial distribution, Tail probabilities 80
Negative hypergeometric distribution 102 103
Nevzorov, V.B. xvi
Neyman — Pearson approach 283
Neyman, J. 283
Ng, K.W. 281
Noncentral distributions 246
Noncentral distributions, Chi-square 246
Noncentral distributions, F 246
Noncentral distributions, t 246
Noncentrality parameter 246
Normal distribution 8 39 53 61 76 81 91 96 170 182 188 207 209—235 239—241 246 257 266 279 282 286
Normal distribution, Asymptotic relations 228
Normal distribution, Bernstein's theorem 221—223
Normal distribution, characteristic function 214 215
Normal distribution, Conditional distributions 219 220
Normal distribution, Convolutions and decompositions 217—219
Normal distribution, Darmois — Skitovitch's theorem 224 226
Normal distribution, Entropy 211
Normal distribution, Helmert's transformation 226 227
Normal distribution, Identity of distributions of linear combinations 227 228
Normal distribution, Independence of linear combinations 220 221
Normal distribution, Introduction 209 210
Normal distribution, Mode 211
Normal distribution, Moments 215 216
Normal distribution, Notations 210 211
Normal distribution, Shape characteristics 217
Normal distribution, Tail behavior 212—214
Normal distribution, Transformations 229—234
Normalized extremes 189—191
Normalized sums 228
Normalizing constants 189—191
Ord, J.K. xv 290 293
Order statistics 114—117 128 135 139 140 157 163 164 174—176 187 205 226 269
Order-preserving transformation 117
Orthogonal linear transformation 264
Orthogonal matrix 264
Panjer, H.H. 74 291
Pareto distribution 133—138 141 283
Pareto distribution, Distributions of minimal values 134 135
Pareto distribution, Entropy 137
Pareto distribution, Introduction 133
Pareto distribution, Moments 136 137
| Pareto distribution, Notations 133
Pareto, V. 283
Pascal distribution 74 102 283
Pascal, B. 283
Patel, J.K. 210 292
Patil, G.P. 98 290 293
Peacock, B. xv 290
Pearson family of distributions 281 283 284
Pearson plane 184
Pearson, E.S. 278 281 283
Pearson, K. 8 283 284 292
Perks, W.F. 206 292
Platykurtic distribution 8 53 110 125 147 154
Podgorski, K. 169 291
Poisson distribution 39 60 61 81 88—100 179 180 209 219 228 256 284 285
Poisson distribution, Conditional probabilities 94 95
Poisson distribution, Convolutions 92
Poisson distribution, Decompositions 92
Poisson distribution, Generating function and characteristic function 90
Poisson distribution, Introduction 89
Poisson distribution, Limiting distribution 96
Poisson distribution, Maximal probability 95
Poisson distribution, Mixtures 96—99
Poisson distribution, Moments 90 91
Poisson distribution, Notations 89
Poisson distribution, Rao — Rubin characterization 99
Poisson distribution, Tail probabilities 91 92
Poisson, S.-D. 284
Poisson-stopped-sum distribution 98—100
Polar coordinates 229
Polar transformation 229
Polya criterion 126
Polya distribution 101 102 284
Polya urn scheme 102 103
Power 246
Power distribution 127—133 135 136 140 147 149
Power distribution, Characteristic function 131
Power distribution, Distributions of maximal values 128
Power distribution, Entropy 131
Power distribution, Introduction 127
Power distribution, Moments 129
Power distribution, Notations 127
Probability integral transform 112 155 203
Probability measure 1 15
Probability space 1 3 15
Proctor, J.W. 114 292
Quadratic form 259—261
Quantile density function 3
Quantile function 3 242
Queueing theory 39
Raikov, D. 36 92 292
random number generation 30 112
Random processes 152
Ranulac, B. 36 291
Rao — Rubin characterization 99 285
Rao, C.R. 99 282 285 293
Rayleigh 285
Rayleigh distribution 192 229 232 277 285
Read, C.B. 210 292
Rectangular distribution 108
Recurrence relation 131 160 175—177 180
Regression 21 253 268
Reliability problems 196
Reproductive property 231
Restricted generalized Poisson distribution 100
Reverse J-shaped 160
Richards, D.St.P. 270 276 290
Riemann zeta function 200
Robustness 286
Rubin, H. 99 293
Run-related distributions 72
Ryzhik, I.M. 31 290
Same type of distribution 4 6 30
Sample mean 225 238 240 246
Sample variance 225
Sarabia, J.-M. 18 289
Scale parameter 4 30 127 134 158 169 173 184 185 190 198 211 216 272
Sech-squared distribution 198
Second law of Laplace 211
Sen, A. 68 293
Service times 39
Seshadri, V. 238 293
Shanbhag, D.N. 285
Shape parameter 127 134 182 184 286
Shepp's result 230
Shepp, L. 230 293
Shimizu, K. 234 290
Skewed distribution 7 8 66 76 91 125 147 160 182 206 207 238
Skewed distribution, Negatively 8 125 147 206 207
Skewed distribution, Positively 8 66 76 91 125 147 160 182 206 238
skewness 7 8 44 52 53 66 76 91 110 125 129 147 154 160 172 182 201 238 241 283
Skitovitch, V.P. 224 293
Snedecor distribution 286
Snedecor, G. W. 245 285 286 293
Spacings 146 163
Srivastava, A.B.L. 99 293
Srivastava, R.C 99 293
Stable distribution 14 121 214 233 236
Standard deviation 233
Statistical modelling 3
Stuart, A. xv 293
Stuttering Poisson distribution 98
Symmetric distribution 8 44 140 154 169 171—173 176 201 205 207 241
Symmetric positive definite matrix 259 260
Symmetric uniform distribution 110 126
t distribution 8 232 240—245 280 286
t test 246 280
Tail probabilities 59 64 80 91 92
Theorem of total probability 57
Theory of errors 211
Tippett, L.H.C 280
Tong, Y.L. 259 293
Transformation 24 25 121 140 141 151 157 170 210 229—234 264 265 269—273 275 286
Triangular distribution 111 117 123—126
Triangular distribution, Characteristic function 125 126
Triangular distribution, Introduction 123
Triangular distribution, Moments 124 125
Triangular distribution, Notations 123
Trinomial distribution 250
Truncated distribution 204
Tukey's lambda distribution 118
Tukey's symmetric lambda distribution 118 286
Tukey, J.W. 118 286 293
Two-tailed exponential distribution 170
Type III line 184
Type VI distribution 245
Type VII distribution 240
U-shaped curve 141 151 154
Uniform distribution 37 107—119 123 127 128 131 133 136 139 140 147 149 163 164 186 187 189 203 229 231 269 270 277 286
Uniform distribution, Characteristic function 110
Uniform distribution, Convolutions 111
Uniform distribution, Decompositions 111
Uniform distribution, Distributions of minima and maxima 113
Uniform distribution, Entropy 110
Uniform distribution, Introduction 107
Uniform distribution, Moments 108
Uniform distribution, Notations 107
Uniform distribution, Order statistics 114—117
Uniform distribution, Probability integral transform 112
Uniform distribution, Relationships with other distributions 117 118
Uniform spacings 146 269 270
Unimodal distribution 7
Urn interpretation 84
Variance 5 7 20 30 40 44 50 52 72 100 103 109 115 118 124 129 137 145 154 160 164 171 182 192 203 205 211 216 217 220 227 234 239 241 245 246 255 259 268
Verhulst, P.J. 197 293
Volkmer, H. 230 289
von Mises, R. 280
Weibull, W. 286
Weibull-type distribution 191 229 287
Weighted distribution 28
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