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概率与统计史研究（二十八）：数理统计中若干展开式的历史AI 解读

This note is concerned with the history of the expansions known to probabilitists and statisticians as Charlier's A-series and Edgeworth's series. It has been pointed out (Gnedenko & Kolmogorov, 1968, Chapter 8) that both these types of expansions appear already in the mathematical work of Tchebychev, so that the names usually attached to them are historically incorrect. In the sequel we shall, however, denote them by the names familiar to statisticians. Both expansions are…

随机变量与概率分布AI 解读

Preface to the first edition Preface to the second edition Preface to the third edition Abbreviations Part I. Principles: 1. Introductory remarks 2. Axioms and preliminary theorems Part II. Distributions in R1: 3. General properties 4. Characteristic functions 5. Addition of independent variables 6. The normal distribution and the central limit theorem 7. Error estimation 8. A class of stochastic processes Part III. Distributions in R2: 9. General properties 10. The normal…