Normal view MARC view

Handbook of the normal distribution

Author: Patel, Jagdish K. ; Read, Campbell B. Series: Statistics: textbooks and monographs ; 150 Publisher: Dekker, 1996.Edition: 2nd revised and expanded ed.Language: EnglishDescription: 431 p. ; 24 cm.ISBN: 0824793420Type of document: BookBibliography/Index: Includes bibliographical references and index
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Item type Current location Collection Call number Status Date due Barcode Item holds
Book Europe Campus
Main Collection
Print QA273.6 .P38 1996
(Browse shelf)
001242942
Available 001242942
Total holds: 0

Includes bibliographical references and index

Digitized

Handbook of the Normal Distribution Contents PREFACE TO THE SECOND EDITION PREFACE TO THE FIRST EDITION 1. GENESIS: A HISTORICAL BACKGROUND 2. BASIC PROPERTIES 2.1 Definitions and Properties 2.2 Moments, Cumulants, and Generating Functions 2.3 Member of Some Families of Distributions 2.4 Some Basic Distributions Derived from the Normal 2.5 Normal Integrals 2.6 Tables References 3. EXPANSIONS AND ALGORITHMS 3.1 Nomograms and Computing Algorithms 3.2 The Standard Normal Density Function 3.3 Expressions Relating to the Distribution Function­ I 3.4 The Distribution Function ­ II 3.5 The Distribution Function­ III 3.6 Approximations Relating to Mills' Ratio: Expansions 3.7 Further Expressions Relating to Mills' Ratio 3.8 From Mills' Ratio to the Distribution Function 3.9 Quantiles 3.10 Approximating the Normal by Other Distributions References 4. CHARACTERIZATIONS 4.1 Characterizations by Linear Statistics 4.2 Linear and Quadratic Characterizations 4.3 Characterizations by Conditional Distributions and Regression Properties 4.4 Independence of Some Statistics 4.5 Characteristic Functions and Moments 4.6 Characterizations from Properties of Transformations 4.7 Sufficiency, Estimation, and Testing 4.8 Miscellaneous Characterizations 4.9 Near-characterizations References iii 1 19 19 24 26 31 34 37 40 45 45 47 48 51 53 55 62 63 66 70 73 81 82 85 88 92 94 96 99 103 105 106 5. SAMPLING DISTRIBUTIONS 5.1 Samples not Larger than Four 5.2 The Sample Mean: Independence 5.3 Sampling Distributions Related to Chi-Square 5.4 Sampling Distributions Related to t 5.5 Distributions Related to F 5.6 The Sample Mean Deviation 5.7 The Moment Ratios Vb1 and b2 5.8 Miscellaneous Results References 6. LIMIT THEOREMS AND EXPANSIONS 6.1 Classical Central Limit Theorems 6.2 Further Central Limit Theorems 6.3 Asymptotic Normality 6.4 Rapidity of Convergence to Normality 6.5 Limit Theorems for Sample Fractiles 6.6 Expansions References 7. NORMAL APPROXIMATIONS TO DISTRIBUTIONS 7.1 The Binomial Distribution 7.2 The Poisson Distribution 7.3 The Negative Binomial Distribution 7.4 The Hypergeometric Distribution 7.5 Miscellaneous Discrete Distributions 7.6 The Beta Distribution 7.7 The von Mises Distribution 7.8 The Chi-Squared and Gamma Distributions 7.9 Noncentral Chi-Square 7.10 Student's t Distribution 7.11 Noncentral t 7.12 The F Distribution 7.13 Noncentral F 7.14 Miscellaneous Continuous Distributions 7.15 Normalizing Transformations References 8. ORDER STATISTICS FROM NORMAL SAMPLES 8.1 Order Statistics: Basic Results 8.2 Moments 8.3 Ordered Deviates from the Sample Mean 8.4 The Sample Range 8.5 Quasi-Ranges 8.6 Median and Midrange 8.7 Asymptotic Properties 8.8 Quantiles 8.9 Miscellaneous Results References 113 113 115 116 121 126 129 132 136 139 145 146 151 153 159 165 167 174 179 180 188 191 195 198 199 202 203 210 212 216 218 222 223 226 232 241 242 250 258 263 268 269 273 278 280 287 9. THE BIVARIATE NORMAL DISTRIBUTION 9.1 Definitions and Basic Properties 9.2 Probability Functions and Tables 9.3 Algorithms and Approximations 9.4 Characterizations 9.5 Associated Distributions 9.6 Offset Circles and Ellipses References 10. BIVARIATE NORMAL SAMPLING DISTRIBUTIONS 10.1 BVN Statistics-General 10.2 The Sample Correlation Coefficient R 10.3 Approximations to the Distribution of R References 11. POINT ESTIMATION 11.1 Sufficiency and Completeness 11.2 Estimators of u and Its Functions 11.3 Estimators of 2 and Its Functions 11.4 Joint Estimators of u and 2, and Their Functions 11.5 Estimators of Parametric Functions: Two Samples References 12. STATISTICAL INTERVALS 12.1 Confidence Intervals 12.2 Tolerance Intervals 12.3 Prediction Intervals References INDEX 295 295 301 307 313 316 324 332 341 341 348 353 359 365 365 367 371 374 384 386 391 391 402 413 419 427

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