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



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

јвтор: Kendall M.G.

язык: en

–убрика: ћатематика/¬еро€тность/—татистика и приложени€/

—татус предметного указател€: ”казатель в процессе заполнени€

ed2k: ed2k stats

»здание: second edition

√од издани€: 1945

 оличество страниц: 457

ƒобавлена в каталог: 04.06.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный 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      279Ч280
$\beta_{1}$, $\beta_{2}$ (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      303Ч304
$\chi^{2}$-distribution, generally      290Ч307
$\chi^{2}$-distribution, properties of      292Ч297
$\Gamma$-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.      85Ч86
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      427Ч429
Agreement, coefficient of, significance of      429Ч435
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      308Ч323
Association, generally, coefficients of      310Ч313
Association, generally, illusory      317Ч318
Association, generally, partial      313Ч317
Asymmetrical distributions      10 see
Attributes, sampling of      197Ч201
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)      50Ч52
Average      see "Moan"
Average corrections to moments      74Ч75 see
b, (sampling value of $\beta_{1}$, measure of skewness)      279Ч280
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      175Ч177
Bayes' theorem in estimating proportion of attributes      200
Bayes' theorem, (Exercise 8.5)      203
Bayes' theorem, comparison with maximum likelihood      178Ч180
Bayes' theorem, postulate      176Ч178
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)      143Ч144
Beans, distribution of, Gram Ч 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      187Ч190
Bias in sampling in choosing plants, (Example 8.1)      187Ч188
Bias in sampling in cropreporting, (Example 8.4)      189Ч190
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      116Ч120
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      125Ч126
Binomial distribution, general properties, $\gamma_{1}$ and $\gamma_{2}$ of, (Example 3.17)      82
Binomial distribution, general properties, arising from mixed population      122Ч124
Binomial distribution, general properties, bivariate form      133Ч134
Binomial distribution, general properties, cumulants of, (Exercise 5.1)      135
Binomial distribution, general properties, distribution function of      119Ч120
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 $\eta$      356Ч358
Bivariate binomial distribution      133Ч134
Bivariate Poisson distribution, (Exercise 5.8)      136
Bivariate, frequency-distributions      19Ч22
Bivariate, moments and cumulants      79Ч81
Bivariate, moments and cumulants, k-statistics and cumulants      281Ч283
Bivariate, moments and cumulants, standard errors of      211
Bivariate, normal distribution      22
Bivariate, normal distribution as limit of bivariate binomial      133Ч134
Bivariate, normal distribution, (Example 3.15)      79Ч80
Bivariate, normal distribution, correlation and regression of      334Ч336
Bivariate, normal distribution, moments of, (Exercise 3.15)      89
Bivariate, normal distribution, multivariate form      376Ч377
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)      297Ч299
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)      67Ч68
Cauchy distribution, characteristic function of, (Example 4.2)      95Ч96
Cauchy distribution, distribution of mean of samples from, (Example 10.1)      233Ч234
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      180Ч183
Characteristic functions, as moment-generating functions      54
Characteristic functions, as moment-generating functions in sampling distributions      242Ч246
Characteristic functions, as moment-generating functions, conditions for a function to be      98Ч99
Characteristic functions, as moment-generating functions, general theory of      90Ч115
Characteristic functions, as moment-generating functions, limiting properties of      99Ч104
Characteristic functions, as moment-generating functions, multi-variate      104Ч105
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)      311Ч312
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.      284Ч285
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      318Ч322
Contingency, coefficient of      319
Continuity correction to $\chi^{2}$      303Ч305
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.      85Ч86 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      352Ч353
Correlation, coefficient of multiple correlation      380Ч381
Correlation, coefficient of multiple correlation, sampling of      381Ч385
Correlation, coefficient of partial      368Ч379
Correlation, coefficient of partial in multivariate normal distribution      376Ч378
Correlation, coefficient of partial in terms of coefficients of lower orders      372
Correlation, coefficient of partial, (crime and religion, Example 15.2)      375Ч376
Correlation, coefficient of partial, definition      370
Correlation, coefficient of partial, examples of, (weather and crops, Example 15.1)      373Ч375
Correlation, coefficient of partial, geometrical interpretation      372Ч373
Correlation, coefficient of partial, sampling distribution of      378Ч379
Correlation, coefficient of product-moment, generally      324Ч367
Correlation, definition      329
Correlation, Fisher's transformation of      345
Correlation, in bivariate normal distribution      334
Correlation, intra-class      358Ч362
Correlation, rank, coefficient $\tau$      391Ч393
Correlation, rank, coefficient $\tau$, sampling of      403Ч408 see
Correlation, rank, generally      388Ч421
Correlation, rank, generally, sampling of      394Ч403
Correlation, sampling of      336Ч348
Correlation, Spearman's coefficient      388Ч391
Correlation, standard error of, (Example 9.6)      211
Correlation, tables of (David)      345
Correlation,calculation of      330Ч334
Covariance, definition      79
Covariance, definition, calculation of      330
Covariance, definition, distribution of in normal samples      339Ч342
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 Ч Charlier series      151Ч152 159
Cramer, H., convergence of Gram Ч Charlier series, central limit theorem      181Ч183
Cramer, H., convergence of Gram Ч Charlier series, distribution of a ratio (Exercise 10.8)      252
Cramer, H., convergence of Gram Ч Charlier series, distribution of a ratio (Exercise 10.8), refs., Random Variables and Probability Distributions      114 183 250
Cramer, H., convergence of Gram Ч 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)      189Ч190
Crops, correlation with weather, (Example 15.1)      373
Cuckoo's eggs, distribution of length of, (Exercise 14.13)      366
Cumulants and (multivariate case)      80Ч81
Cumulants of normal distribution      129
Cumulants, calculation of      65Ч68
Cumulants, definition      60
Cumulants, existence of      64Ч65
Cumulants, generating functions for      90
Cumulants, in bivariate case      80
Cumulants, invariantive properties of      61
Cumulants, relations with moments      61Ч64
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      91Ч92
Discontinuous frequency-functions      12
Discontinuous frequency-functions, variate, examples of distribution according to      6Ч7
Dispersion, measures of      38Ч48 see
Distribution curve      36Ч37
Distribution, determination by moments      105Ч110
Distribution, determined by characteristic function      91Ч94
Distribution, functions      12Ч15
Distribution, limiting properties of      99Ч104 110Ч113
Distribution, relation with probability      172Ч173
Distribution, standard distributions      116Ч163 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      84Ч85 285
Edgeworth, F.Y., citing Weldon's dice data, (Table 1.14)      19
Edgeworth, F.Y., citing Weldon's dice data, form of Gram Ч Charlier series      148Ч149
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      199Ч200
Estimates, of proportions of attributes in large samples generally      201Ч203
Estimates, of proportions of attributes of a ranking      421
Euler Ч Maclaurin sum formula      69
Expectation      84 see
Extreme values of sample, distribution of      217Ч222
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      56Ч60
Factorial moments in terms of ordinary moments      57Ч58
Factorial moments of binomial      118
Factorial moments of hypergeometric, (Exercise 5.4)      135
Factorial moments, calculation of      58Ч60
Factorial moments, definition      66
Factorial moments, generating function for      90
Factorial moments, Sheppard's corrections to      77Ч78
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      283Ч284
Finney, D.J., sampling of variance ratio, (Exercise 14.8)      365
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