Statistical Tables, Explained And Applied

Книга Statistical Tables: Exlained and Applied Statistical Tables: Exlained and Applied Книги Математика Автор: Louis Laurencelle, Francois Dupuis Год издания: 2002 Формат: pdf Издат.:World Scientific Publishing Company Страниц: 244 Размер: 11 ISBN: 9810249195 Язык: Английский0 (голосов: 0) Оценка:Contains several new or unpublished tables, such as one on the significance of the correlation coefficient r, one giving the percentiles of the statistic for monotonic variation, and a table of coefficients for the re-conversion of orthogonal polynomials. Introduction. Common abbreviations and notations -- Normal distribution -- Chi-square (x[symbol) distribution -- Student's t distribution with Dunn-Šidák's t and significance table for r -- F distribution -- Studentized range (q) distribution -- Dunnett's t distribution -- [symbol][symbol] (monotonic variation) distribution -- F[symbol] distribution -- Cochran's C distribution -- Orthogonal polynomials -- Binomial distribution -- Number-of-runs distribution -- Random numbers -- Supplementary examples -- Mathematical complement. Beta [Beta distribution [symbol][symbol](a, b), Beta function B(a, b)] -- Binomial expansion -- Combinations, C(m, n) or ([symbol]) -- Correlation coefficient, [symbol]xy, [symbol]xy -- Distribution function, P(x) -- Expectation (of a random variable), [symbol] or E(X) -- Exponential distribution, E([symbol]) -- Factorial (function), n! -- Factorial (ascending n[symbol], descending n[symbol]) -- Gamma [Gamma distribution G[symbol](x), Gamma function [symbol] (x))] -- Integration (analytic, direct) -- Integration (numerical) -- Interpolation (linear, harmonic) -- Mean (of a random variable), [symbol] or E(X), [symbol] -- Moments of a distribution [[symbol], [symbol], [symbol], [symbol]] -- Moment estimates [[symbol], s[symbol], g[symbol], g[symbol]] -- Poisson distribution, Po([symbol][symbol]) -- Probability density function, p(x) -- Probability distribution function, P(x) -- Simpson's (parabolic) rule -- Standard deviation (of a random variable), [symbol], s -- Uniform distribution, U(a, b) and [symbol](0,1) -- Variance (of a random variable), [symbol][symbol] or var(X), s[symbol] "This book contains several new or unpublished tables, such as one on the significance of the correlation coefficient r, one giving the percentiles of the statistic for monotonic variation (with two structural models of variation), an extensive table for the number-of-runs test, three tables for the binomial sum of probabilities, and a table of coefficients for the re-conversion of orthogonal polynomials." "In the case of the more familiar tables, such as those of the normal integral, or Student's t, Chi-square and F percentiles, all values have been re-computed, occasionally with the authors' own algorithms, using the most accurate methods available today." "For each of the fifteen distributions in the book, the authors have gathered the essential information so that interested readers can handle by themselves all phases of the computations." "An appendix, containing supplementary examples that pertain to the various tables, helps to complete the authors' review of current hypothesis-testing procedures. A mini-dictionary of often-used concepts and methods, statistical as well as mathematical, completes the book." "Besides meeting the needs of practitioners of inferential statistics, this book should be helpful to statistics teachers as well as graduate students, researchers and professionals in scientific computing, who will all find it a rich source of essential data and references on the more important statistical distributions."--BOOK JACKET This book contains several new or unpublished tables, such as one on the significance of the correlation coefficient r, one giving the percentiles of the Ē2 statistic for monotonic variation (with two structural models of variation), an extensive table for the number-of-runs test, three tables for the binomial sum of probabilities, and a table of coefficients for the re-conversion of orthogonal polynomials.In the case of the more familiar tables, such as those of the normal integral, or Student's t, Chi-square and F percentiles, all values have been re-computed, occasionally with the authors'own algorithms, using the most accurate methods available today.For each of the fifteen distributions in the book, the authors have gathered the essential information so that interested readers can handle by themselves all phases of the computations.An appendix, containing supplementary examples that pertain to the various tables, helps to complete the authors'review of current hypothesis-testing procedures. A mini-dictionary of often-used concepts and methods, statistical as well as mathematical, completes the book.Besides meeting the needs of practitioners of inferential statistics, this book should be helpful to statistics teachers as well as graduate students, researchers and professionals in scientific computing, who will all find it a rich source of essential data and references on the more important statistical distributions. Contents......Page 6 Introduction......Page 8 Common abbreviations and notations......Page 10 Normal distribution......Page 11 Chi-square (x2) distribution......Page 27 Student's t distribution......Page 37 F distribution......Page 53 Studentized range (q) distribution......Page 73 Dunnett's t distribution......Page 83 E2 (monotonic variation) distribution......Page 95 Fmax distribution......Page 113 Cochran's C distribution......Page 123 Orthogonal polynomials......Page 135 Binomial distribution......Page 157 Number-of-runs distribution......Page 179 Random numbers......Page 195 Supplementary examples......Page 207 Mathematical complements......Page 221 Binomial expansion......Page 223 Distribution function P(x)......Page 224 Factorial (ascending n(m) descending n(m))......Page 225 Integration (analytic direct)......Page 226 Interpolation (linear harmonic)......Page 227 Moments of a distribution [u o2 Yl Y2]......Page 228 Moment estimates [X s2 g1 g2]......Page 229 Simpson's (parabolic) rule......Page 230 Uniform distribution U(ab) and U(01)......Page 231 Variance (of a random variable) o2 or var(X) s2......Page 232 Bibliographical references......Page 233 Index of examples......Page 237 General index......Page 241