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Handbook of the Normal Distribution（旧版）.pdf
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书名：《Handbook of THE NORMAL DISTRIBUTION》
作者：Jagdish K. Patel & Campbell B. Read
目录：
PREFACE
1 GENESIS: A HISTORICAL BACKGROUND
2 SOME BASIC AND MISCELLANEOUS RESULTS
2.1 Definitions and Properties
2.2 Moments, Cumulants, and Generating Functions
2.3 Distributions Related to PHI(x)
2.4 Member of Some Well-known Families of Distribution
2.5 Compound and Mixed Normal Distribution
2.6 Folded and Truncated Normal Distributions: Mills', Ratio
2.7 "Normal" Distributions on the Circle
References
3 THE NORtvIAL DISTRIBUTION: TABLES, EXPANSIONS,
AND ALGORITHMS
3.1 Tables, Nomograms, and Algorithms
3.2 Expressions for the Distribution Function
3.3 Expressions for the Density Function
3.4 Continued Fraction Expansions: Mills' Ratio
3.S Expressions for Mills' Ratio, Based on Expansions
3.6 Other Approximations to Mills' Ratio
3.7 Inequalities for Mills' Ratio and Other
Quantities
3.8 Quantiles
3.9 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 Other 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
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 sqrt(b1) and b2
5.8 Miscellaneous Results
References
6 LIMIT THEOREMS AND EXPANSIONS
6.1 Central Limit Theorems for Independent
Variables
6.2 Further Limit Theorems
6.3 Rapidity of Convergence to Normality
6.4 Expansions
References
7 NORMAL APPROXIMATIONS TO DISTRIBUTIONS
7.1The Binomial Distribution
7,2The Poisson Distribution
7.3The Negative Binomial Distribution
7.4The Hypergeometric Distribution
7.5Miscellaneous Discrete Distributions
7.6The Beta Distribution
7.7The von Mises Distribution
7.8The Chi-Square and Gamma Distributions
7.9Noncentral Chi-Square
7.10Student's t Distribution
7.11Noncentral t
7.12The F Distribution
7.13Noncentral F
7.14Miscellaneous Continuous Distributions Normalizing
7.15Normalizing Transformations
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 Quant il es
8.8 Miscellaneous Results
References
9 THE WIENER AND GAUSSIAN PROCESSES
9.1 Brownian Motion
9.2 The Wiener Process
9.3 Wiener Process with Absorbing Barriers
9.4 Gaussian Processes
9.5 The Ornstein-Uhlenbeck Process
References
10 THE BIVARIATE NORMAL DISTRIBUTION
10.1Definitions and Basic Properties
10.2Tables and Algorithms
10.3Offset Circles and Ellipses
10.4Moments
10.5Sampling Distributions
10.6Miscellaneous Results
INDEX
References
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