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Bowman K.O., Shenton L.R. — Continued Fractions in Statistical Applications |
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Предметный указатель |
2 3 31 100
Accuracy, loss of 140 142 143 256 264
Additivity 163
Aitken 28 164 298 303
Anomolous 74 96 137 218
Approximant 8
Approximations 10 306
Argument 9
Astronomy 12
Asymptotic series 35 44 94
Asymptotic variance 7
Bernoulli number 44 106 142 149 182
Bessel function 48
binomial 4 29 48 56 274 278
Bivariate 9
Borel modified 264 275
Borel — Pade algorithm 246
Borel — Pade algorithm, 2cB 114—117 259—262 265 269 277 284 286—288
Borel — Pade algorithm, 3cB 264 281
Borel — Pade algorithm, lcB 254 257 275
Boundary condition 258
Bounding sequence 104
Carleman 41 44 47 48 136
Central diagonals 6
chebyshev 16
Coefficient of variation 305
COETS 95 121 142 143 295 304
Complementary 8
Complex coefficient 28
Confidence region 287
Confluent 166 186 195 218 225
Confluent hypergeometric 11
Conjectured bound 105
Conjectures 98 104 117
Consistency 15
Contiguous 171
Continuant 6 177 307 308
Continued fraction, 2nd order 161—193
Continued fraction, 2nd order, as continuant ratio 174
Continued fraction, 2nd order, complex error function 208
Continued fraction, 2nd order, convergence 170
Continued fraction, 2nd order, general theorem 178 189
Continued fraction, 2nd order, recurrences 176—179
Continued fraction, change of origin 63
Continued fraction, equivalence transformation 22
Continued fraction, even and odd parts 21 22
Continued fraction, even and odd parts, 158
Continued fraction, even and odd parts, 54
Continued fraction, even and odd parts, 156
Continued fraction, even and odd parts, 156
Continued fraction, even and odd parts, 210
Continued fraction, even and odd parts, 155
Continued fraction, even and odd parts, 155
Continued fraction, even and odd parts, 160
Continued fraction, even and odd parts, 146
Continued fraction, extending series 75
Continued fraction, form for numerator, 1st order 32
Continued fraction, form for numerator, 2nd order 184
Continued fraction, form for numeratornth order 197—199
Continued fraction, Gauss 26 183 241 242
Continued fraction, infinite 166
Continued fraction, linear transformation 68
Continued fraction, logarithmic integral 45
Continued fraction, Mills'ratio 34 37 49 51 55 56 73 135 166 183
Continued fraction, partial fractions 192 193
Continued fraction, periodic 77 94
Continued fraction, Perron 61 243
Continued fraction, polygamma function 29 212
Continued fraction, special cases of 2nd order 188
Continued fraction, special cases of 3rd order 189
Continued fraction, Stieltjes transform, binomial 29
Continued fraction, Stieltjes transform, gamma density 20 25 38
Continued fraction, Stieltjes transform, hypergeometiric 26 30 241
Continued fraction, Stieltjes transform, negative binomial 48
Continued fraction, Stieltjes transform, psi function 28
Continued fraction, Stieltjes, J.S. 21 161 201
Continued fraction, weight function 77
Convergence region 4
Convergent sequence 133
Convergent Series 60 151 164
Convoluted 119
Correlation 289
Cray 1
Cubic denominantor 206
Decreasing bound 181
Decreasing sequence 104 202 209 212 226 228 231
density 9 40 106 119 121
Derivative 79 84 86 111 138 141 186 295
Derivatives of continued fraction 164 299—302
Descending power 84 149 305
Determinantal function 47
Difference interpolation 88
Differentiability 163
Differential equation 23 35 78 166 258
Divergent series 8 9 10 11 60 95 151 164 218 245
Double factorial 58 95 97 122 246 280
Double integral 111
Efficient estimator 6
Eigenvalue 95
Equivalence transformation 22 35
Equivalent 102
Error function 3 35 208 210
Euler 4 12
Even and odd parts 22 101 188
Even convergent 28
Even part 21 78 80 82 98 147
Expectation 9 99
Explicit 127
Exponential density 112 113 128 142 286 288
Exponential integral 20 140 252 255 256
Exponential population 99
Exponential sampling 95 111 114 116 117 128 141 252 253 262 280
Extended series 75 304
Extrapolate 150
Factorial series 3 4 67 246
Finite difference calculus 5
Finite sum 33
Fluid mechanics 94
FORMAC 150
Fourier coefficient 171
Fourier series 2
Fractional part 83
Fresnel integral 213
Gamma 9 41 95 121 132 141 285 293
Gauss 132 133 227 241 242 305
Gauss continued fraction 26 183 241 242
Gauss form 3
Gaussian density 143
Gaussian type 2
Generating function 39 285
Gram — Charlier 7 26 30 304
Gram — Schmidt 17
Half-Gaussian 143 144
Hamburger 39 41 180 183
hankel 285
hermite 36 84 102
Higher moment 95 106 116 119 292 294
Hyperbolic integral 28
hypergeometric 179
Hypergeometric function 3 26 28 30 35 241
Identities, determinantal 214—217
Identities, extentional 218 223
Imaginary part 210 229 233 235 236
IMPLICIT 11 127 305
Increasing sequence 22 175 190 203 209 212 224 226 228 231 244
Incremental operator 5
Inequality 105 106 147 148 307
Infinite series 95
Inner-product 162 174
| integer arithmetic 146
Integral transform 26 246
Invariant 277
Inverse 18 162 164 246
inversion 127
jacobi 55
Johnson’s 127
Joint distribution 42
kurtosis 7 10 77 111 127 129 130 304
Lagrange 56
Laguerre 15 25 38 41 50
Laplace 219 222
Laplacian expansion 221 224
Least square 23 28
Levin algorithms 108 127 245—246 285
Levin approximant 280 287
Linear algebra 164
Linear transformation 68
Logarithmic density 107
Logarithmic integral 45
Logistic sampling 106
Lower bound 56 148
Macsyma 140
Magnitude 3 35 75 98 106 134
Main diagonal 16
Matrix 18 86 162 163 164 165 199 255 274 277 278 279 282
Matrix product 165 168 169
Maximum likelihood 6 7 42 46 289
Mean square deviation 171
Mills’ ratio 34 37 49 51 55 56 166 183
Mimicry 151 153
Minimal equation 15
Modification 111 159 218 242
Modified transform 77
Moduli 108 122 127
Moment estimator 127 305
Moment generating function 39
Moment problem 31 39 60 161 172
Moment series, , convoluted exponential 119
Moment series, , exponential 111—119 252 253 307
Moment series, , and higher moment normal 149
Moment series, , exponential 95 252 253 288 306
Moment series, , general 9 96
Moment series, , half gaussian 143
Moment series, , logistic 106
Moment series, , normal 98 293
Moment series, , uniform 108
Moment series, , and higher moment gamma 121
Monotone 246
Monotonic 18 22 102 138 230 234 257
Monotonicity 11 97 255
Negative binomial 46 48
Normal distribution 51
Normal integral 135 284
Normal mixture 304
Normal sampling 52 98
Normality 120
Odd convergent 28 41 203
Odd function 102
Odd part 28 66 78 80 82 90 98 131 145 203 238
Operator 89 131 273
Orthogonal polynomial 2 17 13 26 31 40 44 55 69 78 80 97 173 197 305
Orthogonal set 2 3 8 15 20 25 26 28 29 31 69 79 171
Orthogonal system 16 18 24 41 78 80 162 172 195
Oscillation 62
Oscillatory 74 246 285
Overflow 214
Pade algorithm 11
Pade approximant 17 26 52 165 186 187 192 193
Parseval 2 171 172 174 181 195 203 307
Partial denominator 22 33 41 56 170 217
Partial fractions 192 193
Partial numerator 22 55 56 58 60 78 80 83 93 101 104 105 116 124—127 133 147 149 160 170 201 232 263
Partial sums 5 10 62 151 195
Pattern recognition 84
Pearson 151 304
Period 119 122
Periodic 61 77 78 86 89 94
periodicity 104 106 108 293
Perron 32 38 58 78 106 170 182 243 306 307
poisson 31 66 141
Polygamma function 43 44 139 228 234
Polynomials (orthogonal) 197 305
Power series 8 95 99
Principal minor 165 167 174
Psi function 28 42 141
Quadratic denominator 204
Quadrature 9 59 95 137 140 144 151 255 258 264 268 291 295 305
Random 9 42 95
RANGE 10 127 151
Rational forms 198
Rational fraction 12 15 20 60 78 122 127 128 162
Real axis 136 170
Real part 233 236 238
Reciprocal function 103
Reciprocal relations 102
Reciprocal series 50
Reciprocity 103
Reduce 78
Remainder 1 33 38 185
Reversibility 8
Saddle point 38 256 263
Sampling 9
Second order 8 9 24
Series expansion 17 21 35 52
Series sum 10
Shanks 151 152 153 245 262 287
Shape parameter 10 127 305
Sign pattern 62 94 95 103 106 115 119 122 137 147 246 293
Simpson 2 258
Simulation 98 106 114 117 128 252 262 305
Simultaneous estimator 7
Sine and cosine integrals 211
Single factorial 60 256
Singularity 111 115 118 151
skewness 7 10 51 77 111 121 122 127 304
Standard deviation 9 10 95 100 106 111 252 262 280 306
Statistical estimator 6
Step function 31
Sterling’s formula 44 66
Stieltjes, integral 8 12 22 26 41 48 220
Stieltjes, moment problem 12 23 39 62 172 189 194 195 202 218 234
Stieltjes, summability 41
Stieltjes, transform 3 7 31 43 65 66 94 147 219
Stieltjes, transform product 219 221
STUDENT 111 252 306
Sub diagonal 16 192
Summation 10 101 103 122 127 130 151 245
Super diagonal 16 192
symmetric 106 163 165
Symmetric determinant 6 8 166 174 177
System of equation 173
Taylor 9 60 295
Transformation 245
Transient 10
Trapezoidal 2 56
Triangular matrix 279 282
Trigonomitric 49
Triple factorial 128 246
Truncation 50 128 217 218 242
Unbiased 9 305
Underflow 214
uniform 65 108 131 132 133
Upper bound 26 56 148 182
Ursell 8 192 308
Variable 8
Variance 51 60 77 106 107 115 124 125 127 142 305
Weibull distribution 304 305
Weight function 3 15 16 23 29 40 41 55 77 79 94 191
Whittaker 163 298—302
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