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CRC standard probability and statistics tables and formulae / Daniel Zwillinger, Stephen Kokoska.

By: Contributor(s): Material type: TextTextPublisher: Boca Raton : Chapman & Hall/CRC, [2000]Copyright date: ©2000Description: 554 pages : illustrations ; 25 cmContent type:
  • text
Media type:
  • unmediated
Carrier type:
  • volume
ISBN:
  • 1584880597
  • 9781584880592
Other title:
  • Standard probability and statistics tables and formulae
Subject(s): DDC classification:
  • 519.2021 21
LOC classification:
  • QA273.3 .Z95 2000
Contents:
1. Introduction -- 1.1. Background -- 1.2. Data sets -- 1.3. References -- 2. Summarizing Data -- 2.1. Tabular and graphical procedures -- 2.2. Numerical summary measures -- 3. Probability -- 3.1. Algebra of sets -- 3.2. Combinatorial methods -- 3.3. Probability -- 3.4. Random variables -- 3.5. Mathematical expectation -- 3.6. Multivariate distributions -- 3.7. Inequalities -- 4. Functions of Random Variables -- 4.1. Finding the probability distribution -- 4.2. Sums of random variables -- 4.3. Sampling distributions -- 4.4. Finite population -- 4.5. Theorems -- 4.6. Order statistics -- 4.7. Range and studentized range -- 5. Discrete Probability Distributions -- 5.1. Bernoulli distribution -- 5.2. Beta binomial distribution -- 5.3. Beta Pascal distribution -- 5.4. Binomial distribution -- 5.5. Geometric distribution -- 5.6. Hypergeometric distribution -- 5.7. Multinomial distribution -- 5.8. Negative binomial distribution -- 5.9. Poisson distribution -- 5.10. Rectangular (discrete uniform) distribution -- 6. Continuous Probability Distributions -- 6.1. Arcsin distribution -- 6.2. Beta distribution -- 6.3. Cauchy distribution -- 6.4. Chi-square distribution -- 6.5. Erlang distribution -- 6.6. Exponential distribution -- 6.7. Extreme-value distribution -- 6.8. F distribution -- 6.9. Gamma distribution -- 6.10. Half-normal distribution -- 6.11. Inverse Gaussian (Wald) distribution -- 6.12. Laplace distribution -- 6.13. Logistic distribution -- 6.14. Lognormal distribution -- 6.15. Noncentral chi-square distribution -- 6.16. Noncentral F distribution -- 6.17. Noncentral t distribution -- 6.18. Normal distribution -- 6.19. Normal distribution: multivariate -- 6.20. Pareto distribution -- 6.21. Power function distribution -- 6.22. Rayleigh distribution -- 6.23. t distribution -- 6.24. Triangular distribution -- 6.25. Uniform distribution -- 6.26. Weibull distribution -- 6.27. Relationships among distributions -- 7. Standard Normal Distribution -- 7.1. Density function and related functions -- 7.2. Critical values -- 7.3. Tolerance factors for normal distributions -- 7.4. Operating characteristic curves -- 7.5. Multivariate normal distribution -- 7.6. Distribution of the correlation coefficient -- 7.7. Circular normal probabilities -- 7.8. Circular error probabilities -- 8. Estimation -- 8.1. Definitions -- 8.2. Cramer-Rao inequality -- 8.3. Theorems -- 8.4. The method of moments -- 8.5. The likelihood function -- 8.6. The method of maximum likelihood -- 8.7. Invariance property of MLEs -- 8.8. Different estimators -- 8.9. Estimators for small samples -- 8.10. Estimators for large samples -- 9. Confidence Intervals -- 9.1. Definitions -- 9.2. Common critical values -- 9.3. Sample size calculations -- 9.4. Summary of common confidence intervals -- 9.5. Confidence intervals: one sample -- 9.6. Confidence intervals: two samples -- 9.7. Finite population correction factor -- 10. Hypothesis Testing -- 10.1. Introduction -- 10.2. The Neyman-Pearson lemma -- 10.3. Likelihood ratio tests -- 10.4. Goodness of fit test -- 10.5. Contingency tables -- 10.6. Bartlett's test -- 10.7. Cochran's test -- 10.8. Number of observations required -- 10.9. Critical values for testing outliers -- 10.10. Significance test in 2 [times] 2 contingency tables -- 10.11. Determining values in Bernoulli trials -- 11. Regression Analysis -- 11.1. Simple linear regression -- 11.2. Multiple linear regression -- 11.3. Orthogonal polynomials -- 12. Analysis of Variance -- 12.1. One-way anova -- 12.2. Two-way anova -- 12.3. Three-factor experiments -- 12.4. Manova -- 12.5. Factor analysis -- 12.6. Latin square design -- 13. Experimental Design -- 13.1. Latin squares -- 13.2. Graeco-Latin squares -- 13.3. Block designs -- 13.4. Factorial experimentation: 2 factors -- 13.5. 2[superscript r] Factorial experiments -- 13.6. Confounding in 2[superscript n] factorial experiments -- 13.7. Tables for design of experiments -- 13.8. References -- 14. Nonparametric Statistics -- 14.1. Friedman test for randomized block design -- 14.2. Kendall's rank correlation coefficient -- 14.3. Kolmogorov-Smirnoff tests -- 14.4. Kruskal-Wallis test -- 14.5. The runs test -- 14.6. The sign test -- 14.7. Spearman's rank correlation coefficient -- 14.8. Wilcoxon matched-pairs signed-ranks test -- 14.9. Wilcoxon rank-sum (Mann-Whitney) test -- 14.10. Wilcoxon signed-rank test -- 15. Quality Control and Risk Analysis -- 15.1. Quality assurance -- 15.2. Acceptance sampling -- 15.3. Reliability -- 15.4. Risk analysis and decision rules -- 16. General Linear Models -- 16.1. Notation -- 16.2. The general linear model -- 16.3. Summary of rules for matrix operations -- 16.4. Quadratic forms -- 16.5. General linear hypothesis of full rank -- 16.6. General linear model of less than full rank -- 17. Miscellaneous Topics -- 17.1. Geometric probability -- 17.2. Information and communication theory -- 17.3. Kalman filtering -- 17.4. Large deviations (theory of rare events) -- 17.5. Markov chains -- 17.6. Martingales -- 17.7. Measure theoretical probability -- 17.8. Monte Carlo integration techniques -- 17.9. Queuing theory -- 17.10. Random matrix eigenvalues -- 17.11. Random number generation -- 17.12. Resampling methods -- 17.13. Self-similar processes -- 17.14. Signal processing -- 17.15. Stochastic calculus -- 17.16. Classic and interesting problems -- 17.17. Electronic resources -- 17.18. Tables -- 18. Special Functions -- 18.1. Bessel functions -- 18.2. Beta function -- 18.3. Ceiling and floor functions -- 18.4. Delta function -- 18.5. Error functions -- 18.6. Exponential function -- 18.7. Factorials and Pochhammer's symbol -- 18.8. Gamma function -- 18.9. Hypergeometric functions -- 18.10. Logarithmic functions -- 18.11. Partitions -- 18.12. Signum function -- 18.13. Stirling numbers -- 18.14. Sums of powers of integers -- 18.15. Tables of orthogonal polynomials -- 18.16. References -- Notation -- Index.
Summary: "Many non-statisticians have a use for basic statistics daily, but need to be able to reference tables and use data without getting bogged down by advanced statistical methods. Standard Probability and Statistics: Tables and Formulae presents a modern set of tables for this purpose. Reaching beyond a mere catalog of tables, each table has a textual description and at least one example. The difficulty level is on par with first or second year statistics and is directly applicable to business and engineering."--Publisher description.
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Includes bibliographical references and index.

1. Introduction -- 1.1. Background -- 1.2. Data sets -- 1.3. References -- 2. Summarizing Data -- 2.1. Tabular and graphical procedures -- 2.2. Numerical summary measures -- 3. Probability -- 3.1. Algebra of sets -- 3.2. Combinatorial methods -- 3.3. Probability -- 3.4. Random variables -- 3.5. Mathematical expectation -- 3.6. Multivariate distributions -- 3.7. Inequalities -- 4. Functions of Random Variables -- 4.1. Finding the probability distribution -- 4.2. Sums of random variables -- 4.3. Sampling distributions -- 4.4. Finite population -- 4.5. Theorems -- 4.6. Order statistics -- 4.7. Range and studentized range -- 5. Discrete Probability Distributions -- 5.1. Bernoulli distribution -- 5.2. Beta binomial distribution -- 5.3. Beta Pascal distribution -- 5.4. Binomial distribution -- 5.5. Geometric distribution -- 5.6. Hypergeometric distribution -- 5.7. Multinomial distribution -- 5.8. Negative binomial distribution -- 5.9. Poisson distribution -- 5.10. Rectangular (discrete uniform) distribution -- 6. Continuous Probability Distributions -- 6.1. Arcsin distribution -- 6.2. Beta distribution -- 6.3. Cauchy distribution -- 6.4. Chi-square distribution -- 6.5. Erlang distribution -- 6.6. Exponential distribution -- 6.7. Extreme-value distribution -- 6.8. F distribution -- 6.9. Gamma distribution -- 6.10. Half-normal distribution -- 6.11. Inverse Gaussian (Wald) distribution -- 6.12. Laplace distribution -- 6.13. Logistic distribution -- 6.14. Lognormal distribution -- 6.15. Noncentral chi-square distribution -- 6.16. Noncentral F distribution -- 6.17. Noncentral t distribution -- 6.18. Normal distribution -- 6.19. Normal distribution: multivariate -- 6.20. Pareto distribution -- 6.21. Power function distribution -- 6.22. Rayleigh distribution -- 6.23. t distribution -- 6.24. Triangular distribution -- 6.25. Uniform distribution -- 6.26. Weibull distribution -- 6.27. Relationships among distributions -- 7. Standard Normal Distribution -- 7.1. Density function and related functions -- 7.2. Critical values -- 7.3. Tolerance factors for normal distributions -- 7.4. Operating characteristic curves -- 7.5. Multivariate normal distribution -- 7.6. Distribution of the correlation coefficient -- 7.7. Circular normal probabilities -- 7.8. Circular error probabilities -- 8. Estimation -- 8.1. Definitions -- 8.2. Cramer-Rao inequality -- 8.3. Theorems -- 8.4. The method of moments -- 8.5. The likelihood function -- 8.6. The method of maximum likelihood -- 8.7. Invariance property of MLEs -- 8.8. Different estimators -- 8.9. Estimators for small samples -- 8.10. Estimators for large samples -- 9. Confidence Intervals -- 9.1. Definitions -- 9.2. Common critical values -- 9.3. Sample size calculations -- 9.4. Summary of common confidence intervals -- 9.5. Confidence intervals: one sample -- 9.6. Confidence intervals: two samples -- 9.7. Finite population correction factor -- 10. Hypothesis Testing -- 10.1. Introduction -- 10.2. The Neyman-Pearson lemma -- 10.3. Likelihood ratio tests -- 10.4. Goodness of fit test -- 10.5. Contingency tables -- 10.6. Bartlett's test -- 10.7. Cochran's test -- 10.8. Number of observations required -- 10.9. Critical values for testing outliers -- 10.10. Significance test in 2 [times] 2 contingency tables -- 10.11. Determining values in Bernoulli trials -- 11. Regression Analysis -- 11.1. Simple linear regression -- 11.2. Multiple linear regression -- 11.3. Orthogonal polynomials -- 12. Analysis of Variance -- 12.1. One-way anova -- 12.2. Two-way anova -- 12.3. Three-factor experiments -- 12.4. Manova -- 12.5. Factor analysis -- 12.6. Latin square design -- 13. Experimental Design -- 13.1. Latin squares -- 13.2. Graeco-Latin squares -- 13.3. Block designs -- 13.4. Factorial experimentation: 2 factors -- 13.5. 2[superscript r] Factorial experiments -- 13.6. Confounding in 2[superscript n] factorial experiments -- 13.7. Tables for design of experiments -- 13.8. References -- 14. Nonparametric Statistics -- 14.1. Friedman test for randomized block design -- 14.2. Kendall's rank correlation coefficient -- 14.3. Kolmogorov-Smirnoff tests -- 14.4. Kruskal-Wallis test -- 14.5. The runs test -- 14.6. The sign test -- 14.7. Spearman's rank correlation coefficient -- 14.8. Wilcoxon matched-pairs signed-ranks test -- 14.9. Wilcoxon rank-sum (Mann-Whitney) test -- 14.10. Wilcoxon signed-rank test -- 15. Quality Control and Risk Analysis -- 15.1. Quality assurance -- 15.2. Acceptance sampling -- 15.3. Reliability -- 15.4. Risk analysis and decision rules -- 16. General Linear Models -- 16.1. Notation -- 16.2. The general linear model -- 16.3. Summary of rules for matrix operations -- 16.4. Quadratic forms -- 16.5. General linear hypothesis of full rank -- 16.6. General linear model of less than full rank -- 17. Miscellaneous Topics -- 17.1. Geometric probability -- 17.2. Information and communication theory -- 17.3. Kalman filtering -- 17.4. Large deviations (theory of rare events) -- 17.5. Markov chains -- 17.6. Martingales -- 17.7. Measure theoretical probability -- 17.8. Monte Carlo integration techniques -- 17.9. Queuing theory -- 17.10. Random matrix eigenvalues -- 17.11. Random number generation -- 17.12. Resampling methods -- 17.13. Self-similar processes -- 17.14. Signal processing -- 17.15. Stochastic calculus -- 17.16. Classic and interesting problems -- 17.17. Electronic resources -- 17.18. Tables -- 18. Special Functions -- 18.1. Bessel functions -- 18.2. Beta function -- 18.3. Ceiling and floor functions -- 18.4. Delta function -- 18.5. Error functions -- 18.6. Exponential function -- 18.7. Factorials and Pochhammer's symbol -- 18.8. Gamma function -- 18.9. Hypergeometric functions -- 18.10. Logarithmic functions -- 18.11. Partitions -- 18.12. Signum function -- 18.13. Stirling numbers -- 18.14. Sums of powers of integers -- 18.15. Tables of orthogonal polynomials -- 18.16. References -- Notation -- Index.

"Many non-statisticians have a use for basic statistics daily, but need to be able to reference tables and use data without getting bogged down by advanced statistical methods. Standard Probability and Statistics: Tables and Formulae presents a modern set of tables for this purpose. Reaching beyond a mere catalog of tables, each table has a textual description and at least one example. The difficulty level is on par with first or second year statistics and is directly applicable to business and engineering."--Publisher description.

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