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Kendall M.G. — The advanced theory of statistics (vol. 1)
Kendall M.G. — The advanced theory of statistics (vol. 1)

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Название: The advanced theory of statistics (vol. 1)

Автор: Kendall M.G.

Язык: en

Рубрика: Математика/Вероятность/Статистика и приложения/

Статус предметного указателя: Указатель в процессе заполнения

ed2k: ed2k stats

Издание: second edition

Год издания: 1945

Количество страниц: 457

Добавлена в каталог: 04.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
"Cocked-hat" as synonym for unimodal      29
$\beta_{1}$, $\beta_{2}$ (skewness and kurtosis)      81
$\beta_{1}$, $\beta_{2}$ (skewness and kurtosis), (Exercise 11.17)      289
$\beta_{1}$, $\beta_{2}$ (skewness and kurtosis), generalised $\beta$      82
$\beta_{1}$, $\beta_{2}$ (skewness and kurtosis), sampling distributions of      279—280
$\beta_{1}$, $\beta_{2}$ (skewness and kurtosis), standard errors of      225
$\chi^{2}$-distribution as square contingency      319
$\chi^{2}$-distribution in $2\times2$ tables      303
$\chi^{2}$-distribution, correction for continuity      303—304
$\chi^{2}$-distribution, generally      290—307
$\chi^{2}$-distribution, properties of      292—297
$\Gamma$-function, in summing Poisson series      122
$\gamma_{1}$, $\gamma_{2}$ (skewness and kurtosis)      82
$\kappa$, as criterion of type in Pearson distributions      140
Abortion, distribution of women according to term of, (Table 1.23)      26
Abrupt distributions, corrections for grouping to      79
Abrupt distributions, corrections for grouping to, refs.      85—86
Absolute moments      56
Absolute moments, Liapounoff's inequality for, (Exercise 3.14)      88
Accidents, exemplified by Poisson distribution      124
Adyanthaya, N.K., refs., distribution of frequency constants in small samples, (under Pearson)      228
Age, correlation with highest audible pitch, (Example 14.1)      331
Age, correlation with highest audible pitch, (Table 14.1)      325
Agreement, coefficient of      427—429
Agreement, coefficient of, significance of      429—435
Agricultural Research Institute, Oxford, data from Report of, (Table 1.9)      9
Alcoholism and crime, Goring's data on and health, (Exercise-14.12)      366
Alcoholism and crime, Goring's data on, (Table 14.6)      356
Ammon O., data from (hair and eye-colour), (Table 12.4)      300
Anthropometric Committee of British Association, data from Report of, (Table 1.10)      10
Anthropometric Committee of British Association, data from Report of, (Table 1.7)      8
Antimode, definition of      35
Approximations to sampling distributions      see "Sampling distributions"
Aroian, L.A., fitting of Type B distribution to data, (Example 6.4)      156
Aroian, L.A., fitting of Type B distribution to data, refs., Type B series      160
Arrays, in bivariate distributions      327
Association, generally      308—323
Association, generally, coefficients of      310—313
Association, generally, illusory      317—318
Association, generally, partial      313—317
Asymmetrical distributions      10 see
Attributes, sampling of      197—201
Attributes, sampling of in finite populations, (Exercise 8.3)      203
Attributes, sampling of in Poisson distribution, (Exercise 8.2)      203
Australian marriages, $\beta_{1}$ and $\beta_{2}$ of, (Example 3.1)      82
Australian marriages, distribution of, (Table 1.8)      9
Australian marriages, moments of, (Example 3.1)      50—52
Average      see "Moan"
Average corrections to moments      74—75 see
b, (sampling value of $\beta_{1}$, measure of skewness)      279—280
B-function, in summing binomial      120
Babington Smith, B., data from, on random numbers, (Table 8.3)      189
Babington Smith, B., data from, on random numbers, distribution of Spearman's $\rho$, problem of m rankings, method of paired comparisons      436
Babington Smith, B., data from, on random numbers, Random Sampling Numbers      193 197
Babington Smith, B., data from, on random numbers, refs., (under Kendall)      202
Baker, G.A., distribution of means in Type A series, (Exercise 10.7)      252
Bayes' theorem      175—177
Bayes' theorem in estimating proportion of attributes      200
Bayes' theorem, (Exercise 8.5)      203
Bayes' theorem, comparison with maximum likelihood      178—180
Bayes' theorem, postulate      176—178
Bayes, T., refs., doctrine of chances      183
Beans, distribution of, (Table 1.15)      20
Beans, distribution of, fitting of Pearson distribution to, (Example 6.1)      143—144
Beans, distribution of, Gram — Charlier series fitted to, (Example 6.2)      151
Beans, distribution of, histogram of, (Figure 1.4)      20
Bernouilli numbers, footnote      69 71 78
Bernouilli polynomials, definition of      58
Bernstein, S., refs., extension of central limit theorem      183
Bias in sampling      187—190
Bias in sampling in choosing plants, (Example 8.1)      187—188
Bias in sampling in cropreporting, (Example 8.4)      189—190
Bias in sampling in reading randomising machine, (Example 8.3)      189
Bias in sampling in scale reading, (Example 8.2)      188
Binomial distribution, general properties      116—120
Binomial distribution, general properties and (Exercise 5.7)      136
Binomial distribution, general properties in sampling of attributes      198
Binomial distribution, general properties with negative index      125—126
Binomial distribution, general properties, $\gamma_{1}$ and $\gamma_{2}$ of, (Example 3.17)      82
Binomial distribution, general properties, arising from mixed population      122—124
Binomial distribution, general properties, bivariate form      133—134
Binomial distribution, general properties, cumulants of, (Exercise 5.1)      135
Binomial distribution, general properties, distribution function of      119—120
Binomial distribution, general properties, distribution of means of, (Example 10.8)      243
Binomial distribution, general properties, factorial moments of, (Exercise 3.6)      87
Binomial distribution, general properties, incomplete moments of, (Exercises 5.2 and 5.3)      135
Binomial distribution, general properties, limiting form, (Example 4.6)      103
Binomial distribution, moments of      117
Binomial distribution, moments of (Example 3.2)      52
Birth-rates, distribution of in Local Government Areas, (Table 1.1)      3
Birth-rates, distribution of in Local Government Areas, frequency polygon of, (Table 1.1)      4
Biserial $\eta$      356—358
Bivariate binomial distribution      133—134
Bivariate Poisson distribution, (Exercise 5.8)      136
Bivariate, frequency-distributions      19—22
Bivariate, moments and cumulants      79—81
Bivariate, moments and cumulants, k-statistics and cumulants      281—283
Bivariate, moments and cumulants, standard errors of      211
Bivariate, normal distribution      22
Bivariate, normal distribution as limit of bivariate binomial      133—134
Bivariate, normal distribution, (Example 3.15)      79—80
Bivariate, normal distribution, correlation and regression of      334—336
Bivariate, normal distribution, moments of, (Exercise 3.15)      89
Bivariate, normal distribution, multivariate form      376—377
Borel, E., refs., Traite du Calcul des Probabilites      22 183
Bose, S.S., distribution of variance ratio, (Exercise 14.8)      365
Bowley, A.L., refs., F.Y. Edgeworth's Contributions to Mathematical Statistics      160
Bowley, A.L., refs., F.Y. Edgeworth's Contributions to Mathematical Statistics, representative method      202
Brood-mares, distribution of fecundity in, (Table 1.20)      24
Call discount rate, distribution of weekly returns according to, (Table 1.26)      28
Camp, B.H., refs., distribution functions of binomial and hypergeometric      134
Card-shuffling, tested by $\chi^{2}$, (Example 12.1)      297—299
Card-shuffling, tested by $\chi^{2}$, tested by rankings, (Example 16.5)      420
Carleman, T., criteria for uniqueness in the problem of moments      109
Carleman, T., criteria for uniqueness in the problem of moments, refs., Les functions quasi-analytiques      114
Carver, H.C., Sheppard corrections for discrete variables      85
Cauchy distribution, (Example 10.15)      247
Cauchy distribution, (Example 3.12)      67—68
Cauchy distribution, characteristic function of, (Example 4.2)      95—96
Cauchy distribution, distribution of mean of samples from, (Example 10.1)      233—234
Cave, B.M., refs., sampling of correlation coefficient (under Co-operative Study)      363
Census of Population, data from Housing Report, (Table 1.24)      27
Census of Production, data from, on size of firms, (Table 1.17)      23
Central limit theorem      180—183
Characteristic functions, as moment-generating functions      54
Characteristic functions, as moment-generating functions in sampling distributions      242—246
Characteristic functions, as moment-generating functions, conditions for a function to be      98—99
Characteristic functions, as moment-generating functions, general theory of      90—115
Characteristic functions, as moment-generating functions, limiting properties of      99—104
Characteristic functions, as moment-generating functions, multi-variate      104—105
Charlier, C.V.L., Types A and B series      147 see
Charlier, C.V.L., Types A and B series, refs., expansion of frequency functions      160
Cheshire, L., refs., significance of correlation coefficient, (under E.S. Pearson)      363
Chi-square      see "$\chi^{2}$"
Cholera, inoculation against, (Example 13.1)      309
Cholera, inoculation against, (Example 13.2)      311—312
Cholera, inoculation against, (Example 13.3)      313
Cholera, inoculation against, (Table 12.6)      302
Church, A.E.R., sampling moments      256
Church, A.E.R., sampling moments, refs.      284—285
Circular triads, in preferences      423
Class-frequency, definition      2
Class-interval, definition      2
Class-interval, definition, ambiguities in      5
Cloudiness, distribution of days according to, (Table 1.11)      10
Co-operative Study on correlation coefficient, refs.      363
Cochran, W.G., refs., $\chi^{2}$-distribution      305
Coefficients of association, contingency, correlation, etc.      see "Association" "Contingency" "Correlation"
Coin-tossing, as example of sampling of attributes, (Example 8.9)      198
Colligation, coefficient of      311
Combinatorial method, in sampling of k-statistics      see "k-statistics"
Comrie, L.J., refs., Tables of arc, tan x and $log (1+x^{2})$      160
Concentration, coefficient of      43
Concentration, coefficient of and (Figure 2.3)      44
Concentration, coefficient of, curve of      43-44
Concordance, coefficient of      411 see
Consistence, coefficient of      425
Contingency      318—322
Contingency, coefficient of      319
Continuity correction to $\chi^{2}$      303—305
Continuous frequency functions      13
Continuous frequency functions, sampling from      197
Continuum, probability in      170
Cornish, E.A., refs., moments and cumulants in specification of distributions      160
Corrections for grouping in calculation of moments      30 41
Corrections for grouping in calculation of moments, refs.      85—86 see
Corrections for grouping in calculation of moments, when distribution is abrupt      79
Correlation      363
Correlation ratios, definition      351
Correlation ratios, definition for ranked data (Wallis)      437
Correlation ratios, definition, relation with multiple correlation      381
Correlation ratios, definition, sampling distribution in uncorrelated normal population      352—353
Correlation, coefficient of multiple correlation      380—381
Correlation, coefficient of multiple correlation, sampling of      381—385
Correlation, coefficient of partial      368—379
Correlation, coefficient of partial in multivariate normal distribution      376—378
Correlation, coefficient of partial in terms of coefficients of lower orders      372
Correlation, coefficient of partial, (crime and religion, Example 15.2)      375—376
Correlation, coefficient of partial, definition      370
Correlation, coefficient of partial, examples of, (weather and crops, Example 15.1)      373—375
Correlation, coefficient of partial, geometrical interpretation      372—373
Correlation, coefficient of partial, sampling distribution of      378—379
Correlation, coefficient of product-moment, generally      324—367
Correlation, definition      329
Correlation, Fisher's transformation of      345
Correlation, in bivariate normal distribution      334
Correlation, intra-class      358—362
Correlation, rank, coefficient $\tau$      391—393
Correlation, rank, coefficient $\tau$, sampling of      403—408 see
Correlation, rank, generally      388—421
Correlation, rank, generally, sampling of      394—403
Correlation, sampling of      336—348
Correlation, Spearman's coefficient      388—391
Correlation, standard error of, (Example 9.6)      211
Correlation, tables of (David)      345
Correlation,calculation of      330—334
Covariance, definition      79
Covariance, definition, calculation of      330
Covariance, definition, distribution of in normal samples      339—342
Covariance, definition, notation for      204
Cows, distribution of according to age and milk-yield, (Table 1.25)      27
Craig, C.C., corrections to moments of discrete distribution      77
Craig, C.C., corrections to moments of discrete distribution, (Exercise 3.13)      88
Craig, C.C., corrections to moments of discrete distribution, refs.      85
Craig, C.C., corrections to moments of discrete distribution, sampling of cumulants      256
Craig, C.C., corrections to moments of discrete distribution, sampling of cumulants, refs.      285
Cramer, H., convergence of Gram — Charlier series      151—152 159
Cramer, H., convergence of Gram — Charlier series, central limit theorem      181—183
Cramer, H., convergence of Gram — Charlier series, distribution of a ratio (Exercise 10.8)      252
Cramer, H., convergence of Gram — Charlier series, distribution of a ratio (Exercise 10.8), refs., Random Variables and Probability Distributions      114 183 250
Cramer, H., convergence of Gram — Charlier series, refs.      160
Crime and alcoholism, Goring's data on, (Table 14.6)      356
Crime, Goring's data on, correlation with religion, (Example 15.2)      375
Crop-reporters, bias in, (Example 8.4)      189—190
Crops, correlation with weather, (Example 15.1)      373
Cuckoo's eggs, distribution of length of, (Exercise 14.13)      366
Cumulants and (multivariate case)      80—81
Cumulants of normal distribution      129
Cumulants, calculation of      65—68
Cumulants, definition      60
Cumulants, existence of      64—65
Cumulants, generating functions for      90
Cumulants, in bivariate case      80
Cumulants, invariantive properties of      61
Cumulants, relations with moments      61—64
Cumulants, Sheppard's corrections to      78
Cumulative function      90
Curve of concentration      see "Concentration"
Dairy farms, distribution according to coats of milk-production, (Table 1.9)      9
David, F.N., distribution of difference of Type III variates, (Exercise 10.6)      252
David, F.N., distribution of difference of Type III variates, (Exercise 10.6), refs.      363
David, F.N., distribution of difference of Type III variates, (Exercise 10.6), Tables of the Correlation Coefficient      345
Davies, O.L., refs., estimation of standard deviation      228
de Finetti, B., refs., calculation of moan difference      47
de la Vallee Poussin, C.J., refs., Cours d'analyse, footnote      233
Deaf-mutes, distribution of children of, (Table 1.19)      24
Deaths, from scarlet fever, (Table 1.3)      5
Deaths, from scarlet fever, distribution of, according to age at death, (Table 1.12)      11
Deciles, definition      36
Deciles, definition, interdecile range      38
Deciles, definition, standard errors of      225
Degrees of freedom, in $\chi^{2}$-distribution      292
Degrees of freedom, in $\chi^{2}$-distribution in contingency table      299
Demoivre, A., discoverer of normal distribution      131
Denjoy, A., theorem on uniqueness of quasianalytic functions, (Exercise 4.10)      115
Dice, throws with, Weldon's data (Table 1.14)      19
Dice, throws with, Weldon's data, (Example 8.10)      199
Dice, throws with, Weldon's data, (Table 1.16)      23
Dice, throws with, Weldon's data, (Table 12.5)      301
Digits, distribution of, from telephone directory, (Table 1.4)      6
Direct probability      see "Probability"
Dirichlet integrals, in Inversion Theorem      91—92
Discontinuous frequency-functions      12
Discontinuous frequency-functions, variate, examples of distribution according to      6—7
Dispersion, measures of      38—48 see
Distribution curve      36—37
Distribution, determination by moments      105—110
Distribution, determined by characteristic function      91—94
Distribution, functions      12—15
Distribution, limiting properties of      99—104 110—113
Distribution, relation with probability      172—173
Distribution, standard distributions      116—163 see Distributions"
Doerge, K., refs., axiomatisation of von Mises' theory of probability      183
Doodson, A.T., relation of mean, median and mode      35 46
Doodson, A.T., relation of mean, median and mode, refs.      47
Dressel, P.L., refs., seminvarians      84—85 285
Edgeworth, F.Y., citing Weldon's dice data, (Table 1.14)      19
Edgeworth, F.Y., citing Weldon's dice data, form of Gram — Charlier series      148—149
Edgeworth, F.Y., citing Weldon's dice data, refs., law of error      160
Edwards, J., refs., Integral Calculus, footnote      68
Edwards, J., refs., Integral Calculus, footnote and footnote      221
Eells, W.C., formulae for probable errors of correlation coefficients      410
Eells, W.C., formulae for probable errors of correlation coefficients, refs.      436
Egyptian skulls, distribution of, (Table 1.22)      25
Elderton, E.M., data on health of son and alcoholism of father, (Exercise 14.12)      366
Estimates, of proportions of attributes      199—200
Estimates, of proportions of attributes in large samples generally      201—203
Estimates, of proportions of attributes of a ranking      421
Euler — Maclaurin sum formula      69
Expectation      84 see
Extreme values of sample, distribution of      217—222
Eye-colour, rotation with hair-colour in parent and child, (Example 13.4)      314
Eye-colour, rotation with hair-colour, (Example 12.3)      299
Factorial moments      56—60
Factorial moments in terms of ordinary moments      57—58
Factorial moments of binomial      118
Factorial moments of hypergeometric, (Exercise 5.4)      135
Factorial moments, calculation of      58—60
Factorial moments, definition      66
Factorial moments, generating function for      90
Factorial moments, Sheppard's corrections to      77—78
Families deficient in room space, distribution of, (Table 1.24)      27
Fathers, height of, distribution of sons according to, (Table 14.3)      327
Fay, E.A., data from Marriages of the Deaf in America, (Table 1.19)      24
Fecundity, distribution of brood-mares according to, (Table 1.20)      24
Feeding and teeth in infants, (Example 12.5)      304
Fieller, E.C., refs. distribution of a ratio      250
Filon, L.N.G., refs., (under Pearson), standard errors of frequency constants      229
Finite populations, sampling from      283—284
Finney, D.J., sampling of variance ratio, (Exercise 14.8)      365
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