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Aitken A.C. — Statistical mathematics
Aitken A.C. — Statistical mathematics



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Название: Statistical mathematics

Автор: Aitken A.C.

Язык: en

Рубрика: Математика/Вероятность/Статистика и приложения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: fifth edition

Год издания: 1947

Количество страниц: 153

Добавлена в каталог: 28.05.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Addition theorem      13
Additive variate      19 64
Aggregate      10
Algebra of probability      15
Alionation      96
Analysis of variance      54 136—140
Arithmetic mean      30 36 108 109
Arithmetic mean, weight of      109
Authors cited, Bernoulli      50
Authors cited, Bowley      73 75 76 147
Authors cited, Brunt      124
Authors cited, Cauchy      70 71 78 79 133
Authors cited, Charlier      50 54 55 125 128 129
Authors cited, Clopper      127
Authors cited, Colcord and L.S. Doming      136
Authors cited, Coolidge      53 54 55
Authors cited, Copeland      9
Authors cited, Cramer      72
Authors cited, David      142
Authors cited, Doerge      9
Authors cited, Elderton      68
Authors cited, Euler      44
Authors cited, Fisher, E.A.      54 79 92 94 103 105 133—136 138 142 143 144
Authors cited, Frechet      9
Authors cited, Galton      89 99 104 105
Authors cited, Gauss      57
Authors cited, Gillespie      61 71
Authors cited, Gosset      132
Authors cited, Helmert      130
Authors cited, Kapteyn      69
Authors cited, Kendall      25
Authors cited, Keynes      5
Authors cited, Kolmogoroff      9
Authors cited, Legendre      107
Authors cited, Lerch      128
Authors cited, Lexis      52 100
Authors cited, Maclaurin      44
Authors cited, Pearson, E.S.      127
Authors cited, Pearson, K.      37 67—69 71 72 95 100 101 104 128
Authors cited, Poisson      50 51 52 59
Authors cited, Rutherford and Geiger      77 78 103
Authors cited, Sheppard      39 44—47 73 76 94
Authors cited, Tchebychef      115
Authors cited, von Mises      9
Authors cited, Wald      9
Authors cited, Whittaker and Robinson      122 124 145
Authors cited, Yates      105 142 144
Authors cited, Yule      25 106
Authors cited, Yule and Kendall      25
Averages      29 30
Axiomatization      3 4
Bernoullian variance      49 50—54
beta function      71 72
Binomial correlation      82 83
Binomial distribution      49 58 125 133
Binomial distribution of Poisson      50 51 58
Binomial distribution, approximations to      59—61 63
Bivariate distribution      80 86 94 95
Bivariate distribution, generating function      83 84
Blocks, randomized      138 140 141 142
Central factorial moments      43 44 146 147
Central factorials      145 146
Change of origin and scale      23 60
Change of variate      69 135 136 142
Classification      2 5
Coefficient of correlation      86—87 90—93 113—114
Coefficient of perturbation      55
Coefficient, regression      112
Complementary event      13
Complementary event, probability      13
Compound probability      14 15
Computation of moments      39—43
Contingency table      82 83 99 100 102 104 105
Corrections, Sheppard's      39 44—47 73 76 94 142
Correlation      80—103 111 112 113 114 148
Correlation, binomial      82 83
Correlation, coefficient of      86 87 90—93 112—114
Correlation, hypergeometric      84
Correlation, non-linear      95—98
Correlation, non-metrical      99—105
correlation, partial      113 114
Correlation, Poissonian      94 95
Correlation, ratio      95—99
Correlation, surface      82 88
Correlation, table      89—93
Correlation, total      112 113 114
Covariance      84
Criteria of homogeneity      54 55
Cumulant      22 23 32 61 64 65 70 128
Cumulant, factorial      23 64
Cumulant, generating function      22 64 65 67 70
Degrees of freedom      102 103 123 130 131 133 134 137—140 143
Density, probability      16 143
Dependence, functional      88 148
Dependence, linear      101 102 103 130 148
Dependence, statistical      13 14 15 87 88 102 130 148
Dependent events      15 16 56
Deviation, mean absolute      32
Deviation, standard      35 37
Difference of means      134
Differences, finite      59 67 115 118 119 145 146
dispersion      32 34 35
Dispersion, residual      96
Distribution, binomial      49 58 125 133
Distribution, binomial of Poisson      50 51 58
Distribution, bivariate      80 86 94 95
Distribution, Coolidge      53—55
Distribution, frequency      26
Distribution, Gamma type      69 72 102 128
Distribution, Helmert's      130
Distribution, hypergeometric      56 57
Distribution, J-shaped      27 64
Distribution, leptokurtic      38
Distribution, Lexian      53 54 55 72
Distribution, multinomial      55 101
Distribution, multivariate      80 101
Distribution, normal      58—62 72 73 74
Distribution, normal correlated      86—89 101 113
Distribution, of $\chi^{2}$      101 102
Distribution, of Fisher's z      135 136 138
Distribution, of r      92 142 143
Distribution, of Student's t      131—134 143 148
Distribution, of sum of squares      69 129
Distribution, of variance estimate      130—131
Distribution, Pearsonian system      67—71
Distribution, platykurtic      38 71 127 133
Distribution, Poisson      58 59 63 64 66 77 78 103
Distribution, Poisson correlated      94 95
Distribution, probability      26
Distribution, rectangular      48 79
Distribution, sampling      92 125—127 133
Distribution, skew      27 31 36 37 58 69 72 127 131
Distribution, symmetrical      27 61
Distribution, trivariate      80 112 113
Distribution, Type A      58 59 64 65 66 67 73 75 76
Distribution, Type B      58 59 66 67 73 76 77 78
Distribution, Type I      71 72
Distribution, Type III      69 72 102 128 129 130 131
Distribution, U-shaped      27 69 142
Dot diagram      80
Ellipse, probable      88
Empirical formula for $P(\chi^{2})$      104
Equal likeliness      10 11
Equations, normal      110 114 115 116 121
Error function      62 73 74 76 144 147
Error of mean      128
Error of moments      39 126
Error of r      92 143
Error of sampling      39 92 126—129 131 143
Error of variance estimate      129—131
Error, probable      35
Error, standard      39 92 126—129 131 143
Errors and residuals      107 108
Estimation from sample      78 79 143
Euler — Maclaurin formula      44
Events      5 6
Events, dependent      13 15
Events, independent      13 14 15 18
Events, mutually exclusive      13 18
Excess      38 63 131
Expectation, mathematical      21
Factorial cumulant generating function      64
Factorial cumulants      23 64
Factorial moment generating function      22 49 63 84 85
Factorial moments      21 22 41 49 63 84 85 146 147
Factorial polynomials      21 145 146
Factorials and powers      147
Factorials, central      145 146
Finite differences      59 67 115 118 119 145 140
Finite sums      40—43 146
Fitting of harmonic function      120—123
Fitting of polynomial      114—120
Fitting of probability curves      73—78 143
Formulae of interpolation      145 146
Fourfold table      82 85 94 95
Fourier, transform      22
Frequency polygon      28
Frequency, marginal      82 100 102
Frequency, relative      4 5 7 26 60
Function, probability      see "Distribution"
Functional dependence      88 148
Gamma type      see "Distribution"
Generating function      15 16 17 19 148
Generating function, bivariate      53 84
Generating function, change of origin and scale in      23
Generating function, cumulant      22 64 65 67 70
Generating function, factorial cumulant      64
Generating function, factorial moment      22 49 63 84 85
Generating function, moment      20—24 60 65 69 75 84 85 86 101 113
Generating function, multiplication theorem      19 22
Goodness of fit      76 78 100—103 104
Gregory — Newton formula      145
Harmonic regression      81 120—123
Helmert's distribution      130
histogram      28
Homogeneity, criteria of      54 55
Hypergeometric correlation      84
Hypergeometric distribution      56 57
Independence, functional      88 148
Independence, linear      101 148
Independence, statistical      87 148
Independent events      13 14 15 18
Independent frequencies      102 103
Inductive synthesis      3
Integral, probability      62 72 73 133 144 147
Interpolation formulae      145 146
J-shaped curve      27 64
kurtosis      38 63 131 133
Latin square      139—142
Least squares      95 100—108 110 111
Leptokurtic      38
Lexian ratio      55
Lexian variances      53 54 72
Likelihood, maximum      143
Likeliness, equal      10 11
Limit of relative frequency      7 8
Limits of r and $\rho$      87
Linear dependence      101 102 103 130 118
Linear function, of moments      36 37
Linear regression      88 89 106 112
Logic, algebra of      5
Maximum likelihood      143
Mean absolute deviation      32
Mean central factorial      145
Mean square contingency      104—105
Mean square, distribution of      129
Mean, median and mode      30 31 37
Measure of aggregate      10
Median      30 32—34
Minimum variance, principle of      143
Moments      20 31 37 38 see "Generating
Moments, computation of      39—43
Multinomial distribution      55 101
Multiplication theorem      14 15 19
Mutually exclusive events      13 18
Non-linear regression      95 114
Non-metrical correlation      99—105
Normal curve      see "Distribution"
Normal equations      110 114—116 121
Optimal values      108 109
Origin, change of      23 29
Orthogonal functions      116 120 124
Orthogonal polynomials      115 116 120 124
Parameters, estimate of      78 79 143
Partial correlation      113 114
Pearson curves      67—71
Pearsonian coefficient r      86 87 90—93
Periodic regression      81 120—123
Perturbation, coefficient of      55
Phase aggregate      10 12 14
Platykurtic      38 71 127 133
Poisson binomial      see "Distribution"
Polynomial regression      81 114 116—120
Polynomial, factorial      21 145 146
Population      24 25
Powers and factorials      147
PRECISION      107 108
Preparation of normal equations      110
Prismogram      81
probability      4—12
Probability of dependent events      15
Probability, a priori      6 9
Probability, as limit of relative frequency      7 8
Probability, as measure of sub-aggregate      10 12
Probability, complementary      13
Probability, continuous      12
Probability, curve      27
Probability, definition      6 9 12
Probability, density      16
Probability, distribution      see "Distribution"
Probability, function      16
Probability, fundamental theorems      13 14 15
Probability, integral      62 72 73 133 144 147
Probability, marginal      82 100 102
Probability, parameters      29 30
Probability, polygon      28
Probability, total      13 82
Probable error      35
Product-moment      84 86 87 90
Provisional mean      39
Quartiles      34 35 37
Randomized blocks      138 140 142
Randomness      9
RANGE      35 36
Ratio of $\chi^{2}$ variates      135
Ratio, correlation      95—99
Ratio, Lexian      55
Ratio, Student's      131 134 143 148
Rectangular distribution      48 79
Regression      80—82 88 89 95 106 112—124
Regression, coefficients      112
Regression, lines and planes      88—89 106 112
Relative frequency      4 5 7 26 60
Replacement, sampling without      56
Residual      108
Residual, dispersion      96
Residual, variance      109 119 123
Sample      24 25 86 107 125—135
Sample, estimation from      78 79 143
Sampling distribution      92 125—135 143 148
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