正态分布两发现过程的数学文化比较Comparision of mathematical culture in processes about the discovery of normal distribution
徐传胜;张梅东;
摘要(Abstract)：
正态分布是概率论中最重要的分布,它分别由棣莫弗和高斯各自独立导出,其发现极大的促进了概率论和数理统计的发展.对正态分布两推导过程所蕴含的概率思想及创新点进行了详细分析.另外,还比较了其不同的数学文化背景.
关键词(KeyWords)： 正态分布;概率论;无穷级数;二项分布;误差函数
基金项目(Foundation): 国家自然科学基金资助项目(10471111);; 吴文俊丝绸之路天元基金项目
作者(Authors): 徐传胜;张梅东;
参考文献(References)：
- [1]Lancaster H O.Encyclopedia of Statistical Science[M].New York:Wiley,1988.
- [2]Hacking I.The Taming of Chance[M].New York:Cambridge University Press,1990.
- [3]Cohen I B.Revolution in Science[M].Cambridge:The Belknap Press of Harvard University Press,1985.
- [4]Todhunter I.A History of the Mathematical of Theory of Probability from the Times of Pascal to thatof Laplace[M].New York:Chelsea,1965.
- [5]Stigler S M.The History of Statistics[M].Cambridge:Harvard University Press,1986.
- [6]莫里斯.克莱因[美].古今数学思想[M].上海:上海科学技术出版社,2000.
- [7]Plackett R L.The Discovery of the Method of Least Squares[M].Biometrika,1972,59:239-251..
- [8]Sheynin O B.C.F.Gauss and the theory of error[J].Archive for History of Exact Science,1979,20:21-72.
- [9]Katz Victor J.数学史通论[M].李文林,邹建成,胥鸣伟,译.2nd ed.北京:高等教育出版社,2004,2.
- [10]Waterhouse W C.Gauss′s first argument for least squares[J].Archive for History of Exact Science,1991,41:41-52.
- [11]Rabinovitch N L.Probability and Statistical Inference in Ancient and Medieval Jewish Literature[M].Toroto:Niversity of Toronto Press,1973.
- [12]De Moiver.The Doctrine of Chances[M].London:[s.n.],1927.
- [13]Hacking I.Abraham De Moiver[J].Discovery of Scientific Biograph,1974,19:135-136.