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Balakrishnan N., Nevzorov V.B. — A Primer on Statistical Distributions
Balakrishnan N., Nevzorov V.B. — A Primer on Statistical Distributions



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Название: A Primer on Statistical Distributions

Авторы: Balakrishnan N., Nevzorov V.B.

Аннотация:

Designed as an introduction to statistical distribution theory.
* Includes a first chapter on basic notations and definitions that are essential to working with distributions.
* Remaining chapters are divided into three parts: Discrete Distributions, Continuous Distributions, and Multivariate Distributions.
* Exercises are incorporated throughout the text in order to enhance understanding of materials just taught.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 328

Добавлена в каталог: 09.10.2007

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$S_B$ distribution      281
$S_U$ distribution      281
$\sigma$-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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