Kendall's advanced theory of statistics 1 Distribution theory
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| Sprache: | English |
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1994
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| Ausgabe: | 6. ed. |
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| 245 | 1 | 0 | |a Kendall's advanced theory of statistics |n 1 |p Distribution theory |c orig. by Maurice Kendall |
| 250 | |a 6. ed. | ||
| 264 | 1 | |a London u.a. |b Arnold |c 1994 | |
| 300 | |a XX, 676 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 700 | 1 | |a Stuart, Alan |d 1922-1998 |e Sonstige |0 (DE-588)133255557 |4 oth | |
| 700 | 1 | |a Ord, John Keith |d 1942- |e Sonstige |0 (DE-588)13325562X |4 oth | |
| 700 | 1 | |a Kendall, Maurice G. |d 1907-1983 |e Sonstige |0 (DE-588)122372778 |4 oth | |
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Datensatz im Suchindex
| _version_ | 1819583167043993600 |
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| adam_text | Titel: Bd. 1. The advanced theory of statistics. Distribution theory
Autor:
Jahr: 1994
CONTENTS
Chapter Page
List of Examples in Text xi
Introductory Note xvii
Glossary of Abbreviations xx
1 Frequency Distributions 1
Frequency distributions, 1.5; Discrete variâtes, 1.9; Continuous variâtes, 1.10;
Stem-and-leaf plots 1.14; Probability functions and distribution functions, 1.15;
Random variables, 1.20; Density smoothing, 1.21; Excursus on integrals, 1.22;
Variate transformations, 1.26; The genesis of distributions, 1.28; Multivariate
distributions, 130; The bivariate case: conditional distributions, 132; Marginal
distributions, 133; Independence, 1.34; Probability generating functions, 1.37;
Exercises 1.1-1.24.
2 Measures of Location and Dispersion 39
Location and scale parameters, 2.2; Measures of location; the arithmetic mean,
2.3; The geometric and harmonic means, 2.5; Comparison of means: standardiza-
tion and weighting, 2.7; The median, 2.8; The mode, 2.10; Choice of location
measure: robustness, 2.12; Quantiles, 2.13; Measures of dispersion, 2.16; Range
and interquantile differences, 2.17; Mean deviation, 2.18; Variance and standard
deviation, 2.19; Computational procedures, 2.20; Sheppard s corrections, 2.21;
Mean difference 2.22; Robust dispersion measures, 2.23; Coefficients of variation:
standardization, 2.24; Concentration, 2.25; Expected values in general, 2.27;
Inequalities, 231; Exercises 2.1-2.31.
3 Moments and Cumulants 74
Moments, 3.1; Calculation of moments, 33; Moment generating functions and
characteristic functions, 3.5; Absolute moments, 3.6: Factorial moments, 3.7;
Evaluation of factorial moments, 3.10; Factorial moment generating functions,
3.11; Cumulants, 3.12; Relations between moments and cumulants, 3.14; Evalua-
tion of cumulants, 3.16; Factorial cumulants, 3.17; Corrections for grouping
(Sheppard s corrections), 3.18; Average corrections 3.20; Sheppard s corrections
for factorial moments, 3.23; Bernoulli numbers and polynomials and Gamma
function formulae, 3.24; Sheppard s corrections for cumulants, 3.25; Negative and
fractional moments, 3.26; Multivariate moments and cumulants, 3.27; Measures
of skewness, 3.31; Kurtosis, 332; Measures of shape, 333; Moments as
characteristics of a distribution, 334; Inequalities of the Chebyshev type, 3.35;
Multivariate inequalities, 3.39; Information measures, 3.40; Distance between
distributions, 3.42; The method of moments, 3.43; Exercises 3.1-333.
4 Characteristic functions 125
The Inversion Theorem, 4.3; Conditions for a function to be a characteristic
function, 4.7; Limiting properties of distribution and characteristic function«.
vU
vili CONTENTS
4.9; The First Limit Theorem, 4.14; Converse of the First Limit Theorem, 4.15;
Multivariate characteristic functions, 4.16; Conditional characteristic functions,
4.19; The problem of moments, 4.20; The Second Limit Theorem, 4.29;
Infinitely divisible and stable characteristic functions, 4.33; Sums of random
variables, 4.42; Exercises 4.1-430.
5 Standard Distributions 163
The binomial distribution, 5.2; Tables of the binomial distribution, 5.7; The
Poisson distribution, 5.8; Tables of the Poisson distribution, 5.9; Generaliza-
tions of the binomial and Poisson, 5.10; Pólya urn scheme: the hypergeometric
distributions, 5.13; Properties of the hypergeometric distribution, 5.14; Sequential
sampling: the negative binomial distribution, 5.16; Mixtures of distributions, 5.20;
Distributions modified by the recording process: censoring and truncation, 5.25;
The logarithmic series distribution, 5.28; The uniform distribution, 5.30; The
Poisson process: exponential and Gamma distributions, 531; The Weibull
distribution: hazard rate, 5.33; The normal distribution: c.f. and moments, 5.36;
The normal d.f., 537; Mills ratio, 5.38; Tables of the normal distribution, 5.41;
Properties of the normal distribution, 5.42; Mixtures of normal distributions,
5.44; Generalizations and extensions, 5.46; The exponential family of distribu-
tions, 5.47; Power series distributions, 5.49; Distributions on the circle and on the
sphere, 5.50; Exercises 5.1-533.
6 Systems of Distributions 215
Pearson distributions, 6.2; Chebyshev-Hermite Polynomials, 6.14; The Gram-
Charlier series of Type A, 6.17; Edgeworth s form of the Type A series, 6.18;
Tetrachoric functions, 6.21; Other expansions, 6.24; Polynomial transformations
to normality, 6.25; Functional transformations to normality: Johnson distribu-
tions, 6.27; The lognormal distribution, 6.29; Johnson s SB system, 6.32;
Johnson s Sv system, 6.35; Burr s distributions, 637; Fitting by frequency
moments, 6.39; Distributions specified by hazard rates, 6.42; Exercises 6.1-6.25.
7 Multivariate Distributions 258
Basic structure, 7.2; The multinomial distribution, 7.7; The bivariate binomial
distribution, 7.8; The bivariate Poisson distribution, 7.11; Multivariate urn
schemes, 7.12; Mixture distributions, 7.14; The bivariate uniform distribution,
7.18; The binormal (bivariate normal) distribution, 7.20; Generation of multi-
variate distributions, 7.23; The Dirichlet distributions, 7.26; Bivariate families of
distributions, 7.27; Copulas, 7.33; Hazard rate and NBU distributions, 7.34;
Bivariate distributions with given conditionals, 7.36; Shape distributions, 7.37;
Exercises 7.1-7.27.
8 Probability and Statistical Inference 286
The rules of probability, 8.5; Conditional probability and Bayes Theorem, 8.7;
Equally likely events, 8.9; Frequency theory of probability, 8.11; Logical prob-
ability, 8.12; Subjective probability, 8.14; Countably infinite numbers of events,
8.16; Probability in a continuum, 8.17; Bayes postulate, 8.19; Maximum
Likelihood, 8.22; Noninformative priors, 8.28; Informative priors, 8.30; Con-
jugate priors, 8.31; Random variables, 8.35; Joint and conditional distributions,
8.38; Sums of random variables, 8.40; The Weak Law of Large Numbers, 8.44;
CONTENTS Ix
The Strong Law of Large Numbers, 8.46; The Central Limit theorem, 8.47; Exer-
cises 8.1-833.
9 Random Sampling 318
The. sampling problem, 9.1; Randomness in sampling practice, 9.5; The technique
of random sampling, 9.9; Random sampling numbers, 9.11; Pseudorandom
numbers, 9.19; Random values from specific distributions, 9.22; Sampling for
attributes, 9.28; Standard error, 9.31; Exercises 9.1-9.20.
10 Standard Errors 346
Standard errors of moments, 103; Standard errors of functions of random
variables, 10.5; Standard errors of Divariate moments, 10.9; Standard errors of
quantiles, 10.10; Standard error of the mean deviation, 10.13; Standard error of
the mean difference, 10.14; Some commonly required standard errors, 10.15; The
jackknife and the bootstrap, 10.17; Exercises 10.1-10.29.
11 Exact Sampling Distributions 374
The analytical method, 11.2; Order statistics, 11.4; The geometrical method, 11.5;
The method of characteristic functions, 11.6; The distribution of a sum or differ-
ence of independent random variables, 11.8; The distribution of a ratio or product
of independent random variables, 11.9; Edgeworth and saddlepoint approxima-
tions for sums, 11.13; Exercises 11.1-11.32.
12 Cumulants of Sampling Distributions—(1) 414
Symmetric functions, 12.4; ¿-statistics, 12.6; Expression of Ar-statistics in terms
of symmetric products and sums, 12.9; Sampling cumulants of Ar-statistics, the
combinatorial rules, 12.12; Sampling cumulants of Ar-statistics: the results,
12.16; Sampling cumulants of a ratio, 12.18; Sampling from finite populations,
12.20; Multiple Ar-statistics, 12.22; Exchangeability, 12.23; Exercises 12.1-12.22.
13 Cumulants of Sampling Distributions—(2) 455
Bivariate Ar-statistics, 13.2; Proof of the combinatorial rules, 13.4; The essential
structure of the results, 13.11; Summary of results, 13.15; Tables of symmetric
functions, 13.18; Exercises 13.1-13.13.
14 Order Statistics 475
Distributions in the continuous case, 14.2; The distribution function of an order
statistic, 14.3; Median and quartiles in the standardized normal case, 14.4;
Pearson s expansion, 14.9; Quantiles and extreme values: asymptotic distributions,
14.11; Asymptotic distributions of extreme values, 14.13; The three asymptotes,
14.15; Bivariate and multivariate extremes, 14.18; Asymptotic distributions of mth
extreme values, 14.19; The order statistics in the normal case, 14.21; The general
case, 14.22; Joint distribution of two order statistics, 14.23; Spacings, 14.24;
Ranges and mid-ranges, 14.25; The exact distribution of the range, 14.26; The
asymptotic distribution of the range, 14.27; The reduced range and mid-range,
14.29; Tables for extreme value distributions, 14.31; Exercises 14.1-14.28.
x CONTENTS
13 The Multinormal Distribution and Quadratic Forms 508
Characteristic function and moments, 15.2; Linear functions of normal variâtes,
• 15.4; The multinormal integral, 15.5; Orthant probabilities, 15.10; Quadratic
forms in normal variâtes, 15.14; The decomposition of quadratic forms in
independent normal variâtes, 15.20; Ratios of quadratic forms, 15.26; Charac-
terizations of the normal distribution, 15.30; Exercises 15.1-15.30.
16 Distributions Associated with the Normal 541
The x2 distribution, 16.2; Properties of the x1 distribution, 16.3; Tables of the
X2 distribution, 16.4; Square-root and cube-root transformations of x 16.5;
Student s t distribution, 16.10; Properties of Student s t distribution, 16.11; Tables
of Student s / distribution, 16.13; Fisher s F and z distributions, 16.15; Properties
of the F and z distributions, 16.17; Tables of F and z, 16.19; Relations among
the distributions, 16.22; The bivariate normal (binormal) distribution, 16.23; The
distribution of the sample correlation coefficient, 16.24; Fisher s transformation
of r, 16.33; Distribution of regression coefficients in binormal samples, 16.35; A
conditional approach, 16.37; Robustness, 16.38; Multinormal distribution theory,
16.42; The Wishart distribution, 16.43; The additive property of Wishart distribu-
tions, 16.47; Moments of the generalized variance, 16.49; The correlation determi-
nant, 16.51; Hotelling s T, 16.52; Large sample results, 16.56; The latent roots
of the covariance matrix, 16.57; Large sample results for latent roots, 16.61;
Further results, 16.63; Exercises 16.1-16.41.
Appendix Tables 603
References 615
Matrix of Examples in Text 647
Index (Subjects and Authors) 649
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| spellingShingle | Kendall's advanced theory of statistics |
| title | Kendall's advanced theory of statistics |
| title_auth | Kendall's advanced theory of statistics |
| title_exact_search | Kendall's advanced theory of statistics |
| title_full | Kendall's advanced theory of statistics 1 Distribution theory orig. by Maurice Kendall |
| title_fullStr | Kendall's advanced theory of statistics 1 Distribution theory orig. by Maurice Kendall |
| title_full_unstemmed | Kendall's advanced theory of statistics 1 Distribution theory orig. by Maurice Kendall |
| title_short | Kendall's advanced theory of statistics |
| title_sort | kendall s advanced theory of statistics distribution theory |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006425524&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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