Statistics for physical sciences : an introduction

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Statistics for physical sciences : an introduction / B.R. Martin

資料種別:: 図書
出版情報:: Amsterdam : Elsevier/Academic Press, 2012
形態:: x, 302 p. ; 25 cm
著者名:: Martin, B. R. (Brian Robert) <DA06366457>
ISBN:: 9780123877604 [0123877601]
書誌ID:: BB08228513

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注記:

Includes bibliographical references (p. 293-294) and index

主題:

Physical sciences--Statistical methods

言語:

英語

目次情報:

Preface

Statistics, Experiments, and Data / 1：

Experiments and Observations / 1.1：

Displaying Data / 1.2：

Summarizing Data Numerically / 1.3：

Measures of Location / 1.3.1：

Measures of Spread / 1.3.2：

More than One Variable / 1.3.3：

Large Samples / 1.4：

Experimental Errors / 1.5：

Problems 1

Probability / 2：

Axioms of Probability / 2.1：

Calculus of Probabilities / 2.2：

The Meaning of Probability / 2.3：

Frequency Interpretation / 2.3.1：

Subjective Interpretation / 2.3.2：

Problems 2

Probability Distributions I: Basic Concepts / 3：

Random Variables / 3.1：

Single Variates / 3.2：

Probability Distributions / 3.2.1：

Expectation Values / 3.2.2：

Moment Generating, and Characteristic Functions / 3.2.3：

Several Variates / 3.3：

Joint Probability Distributions / 3.3.1：

Marginal and Conditional Distributions / 3.3.2：

Moments and Expectation Values / 3.3.3：

Functions of a Random Variable / 3.4：

Problems 3

Probability Distributions II: Examples / 4：

Uniform / 4.1：

Univariate Normal (Gaussian) / 4.2：

Multivariate Normal / 4.3：

Bivariate Normal / 4.3.1：

Exponential / 4.4：

Cauchy / 4.5：

Binomial / 4.6：

Multinomial / 4.7：

Poisson / 4.8：

Problems 4

Sampling and Estimation / 5：

Random Samples and Estimators / 5.1：

Sampling Distributions / 5.1.1：

Properties of Point Estimators / 5.1.2：

Estimators for the Mean, Variance, and Covariance / 5.2：

Laws of Large Numbers and the Central Limit Theorem / 5.3：

Propagation of Enors / 5.4：

Problems 5

Sampling Distributions Associated with the Normal Distribution / 6：

Chi-Squared Distribution / 6.1：

Student's t Distribution / 6.2：

F Distribution / 6.3：

Relations Between χ², t, and F Distributions / 6.4：

Problems 6

Parameter Estimation I: Maximum Likelihood and Minimum Variance / 7：

Estimation of a Single Parameter / 7.1：

Variance of an Estimator / 7.2：

Approximate methods / 7.2.1：

Simultaneous Estimation of Several Parameters / 7.3：

Minimum Variance / 7.4：

Parameter Estimation / 7.4.1：

Minimum Variance Bound / 7.4.2：

Problems 7

Parameter Estimation II: Least-Squares and Other Methods / 8：

Unconstrained Linear Least Squares / 8.1：

General Solution for the Parameters / 8.1.1：

Errors on the Parameter Estimates / 8.1.2：

Quality of the Fit / 8.1.3：

Orthogonal Polynomials / 8.1.4：

Fitting a Straight Line / 8.1.5：

Combining Experiments / 8.1.6：

Linear Least Squares with Constraints / 8.2：

Nonlinear Least Squares / 8.3：

Other Methods / 8.4：

Minimum Chi-Square / 8.4.1：

Method of Moments / 8.4.2：

Bayes' Estimators / 8.4.3：

Problems 8

Interval Estimation / 9：

Confidence Intervals: Basic Ideas / 9.1：

Confidence Intervals: General Method / 9.2：

Normal Distribution / 9.3：

Confidence Intervals for the Mean / 9.3.1：

Confidence Intervals for the Variance / 9.3.2：

Confidence Regions for the Mean and Variance / 9.3.3：

Poisson Distribution / 9.4：

Confidence Intervals Near Boundaries / 9.5：

Bayesian Confidence Intervals / 9.7：

Problems 9

Hypothesis Testing I: Parameters / 10：

Statistical Hypotheses / 10.1：

General Hypotheses: Likelihood Ratios / 10.2：

Simple Hypothesis: One Simple Alternative / 10.2.1：

Composite Hypotheses / 10.2.2：

Basic Ideas / 10.3：

Specific Tests / 10.3.2：

Other Distributions / 10.4：

Analysis of Variance / 10.5：

Problems 10

Hypothesis Testing II: Other Tests / 11：

Goodness-of-Fit Tests / 11.1：

Discrete Distributions / 11.1.1：

Continuous Distributions / 11.1.2：

Linear Hypotheses / 11.1.3：

Tests for Independence / 11.2：

Nonparametric Tests / 11.3：

Sign Test / 11.3.1：

Signed-Rank Test / 11.3.2：

Rank-Sum Test / 11.3.3：

Runs Test / 11.3.4：

Rank Correlation Coefficient / 11.3.5：

Problems 11

Miscellaneous Mathematics / Appendix A：

Matrix Algebra / A.1：

Classical Theory of Minima / A.2：

Optimization of Nonlinear Functions / Appendix B：

General Principles / B.1：

Unconstrained Minimization of Functions of One variable / B.2：

Unconstrained Minimization of Multivariable Functions / B.3：

Direct Search Methods / B.3.1：

Gradient Methods / B.3.2：

Constrained Optimization / B.4：

Statistical Tables / Appendix C：

Binomial Distribution / C.1：

Chi-squared Distribution / C.3：

Answers to Odd-Numbered Problems / C.5：

Bibliography

Index

Preface

Statistics, Experiments, and Data / 1：

Experiments and Observations / 1.1：

Displaying Data / 1.2：

Summarizing Data Numerically / 1.3：

Measures of Location / 1.3.1：

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