Inleiding tot de R-statistiek

統計学全般に関する備忘メモの書庫(三中信宏)

『The History of Statistics: The Measurement of Uncertainty before 1900』

Stephen M. Stigler

(1986年刊行,Harvard University PressISBN:0674403401 [hbk] / ISBN:067440341X [pbk] → 版元ページ

統計学史の本として定評があり,版を重ねています.400ページもある厚い本だが,ペーパーバック版であれば,たった二千円ほどで買えます.とても安い買い物です.正規分布ひとつをとっても,どのような経緯であのような関数形が求められたのかが,ラプラスからガウスにいたる流れとして詳しく描かれています.

【目次】

Acknowledgments vii

Introduction 1

PART 1: The Development of Mathematical Statistics in Astronomy and Geodesy before 1827 9

1. Least Squares and the Combination of Observations 11

Legendre in 1805

Cotes's Rule

Tobias Mayer and the Libration of the Moon

Saturn, Jupiter, and Enter

Laplace's Rescue of the Solar System

Roger Boscovich and the Figure of the Earth

Laplace and the Method of Situation

Legendre and the Invention of Least Squares

2. Probabilists and the Measurement of Uncertainty 62

Jacob Bernoulli

De Moivre and the Expanded Binomial

Bernoulli's Failure

De Moivre's Approximation

De Moivre's Deficiency

Simpson and Bayes

Simpson's Crucial Step toward Error

A Bayesian Critique

3. Inverse Probability 99

Laplace and Inverse Probability

The Choice of Means

The Deduction of a Curve of Errors in 1772-1774

The Genesis of Inverse Probability

Laplace's Memoirs 0f 1777 - 1781

The Error Curve of 1777

Bayes and the Binomial

Laplace the Analyst

Nonuniform Prior Distributions

The Central Limit Theorem

4. The Gauss-Laplace Synthesis 139

Gauss in 1809

Reenter Laplace

A Relative Maturity: Laplace and the Tides of the Atmosphere

The Situation in 1827

PART 2: The Struggle to Extend a Calculus of Probabilities to the Social Sciences 159

5. Quetelet's Two Attempts 161

The de Keverberg Dilemma

The Average Man

The Analysis of Conviction Rates

Poisson and the Law of Large Numbers

Poisson and Juries

Comte and Poinsot

Cournot's Critique

The Hypothesis of Elementary Errors

The Fitting of Distributions: Quetelismus

6. Attempts to Revive the Binomial 221

Lexis and Binomial Dispersion

Arbuthnot and the Sex Ratio at Birth

Buckle and Campbell

The Dispersion of Series

Lexis's Analysis and Interpretation

Why Lexis Failed

Lexian Dispersion after Lexis

7. Psychophysics as a Counterpart 239

The Personal Equation

Fechner and the Method of Right and Wrong Cases

Ebbington and Memory

PART 3: A Breakthrough in Studies of Heredity 263

8. The English Breakthrough: Galton 265

Galton, Edgeworth, Pearson

Galton's Hereditary Genius and the Statistical Scale

Conditions for Normality

The Quincunx and a Breakthrough

Reversion

Symmetric Studies of Stature

Data on Brothers

Estimating Variance Components

Galton's Use of Regression

Correlation

9. The Next Generation: Edgeworth 300

The Critics' Reactions to Galton's Work

Pearson's Initial Response

Francis Ysidro Edgeworth

Edgeworth's Early Work in Statistics

The Link with Galton

Edgeworth, Regression, and Correlation

Estimating Correlation Coefficients

Edgeworth's Theorem

10. Pearson and Yule 326

Pearson and Statisticians

The Pearson Family of Curves

Pearson versus Edgeworth

Pearson and Correlation

Yule, the Poor Law, and Least Squares: The Second Synthesis

The Situation in 1900

Appendix A. Syllabus for Edgeworth's 1885 Lectures 363

Appendix B. Syllabus for Edgeworth's 1892 Newmarch Lectures 367

Suggested Readings 370

Bibliography 379

Index 399