Normal distribution - Wikipedia, the free encyclopedia

The normal distribution is considered the most prominent probability distribution in statistics. There are several reasons for this:[1] First, the normal distribution arises from the central limit theorem, which states that under mild conditions, the mean of a large number of random variables independently drawn from the same distribution is distributed approximately normally, irrespective of the form of the original distribution. This gives it exceptionally wide application in, for example, sampling. Secondly, the normal distribution is very tractable analytically, that is, a large number of results involving this distribution can be derived in explicit form.

[1]  J. Rohrbasser,et al.  Wilhelm Lexis: The Normal Length of Life as an Expression of the “Nature of Things” , 2003 .

[2]  G. Marsaglia,et al.  The Ziggurat Method for Generating Random Variables , 2000 .

[3]  S. E. Ahmed,et al.  Handbook of Statistical Distributions with Applications , 2007, Technometrics.

[4]  Statistics on the Table , 2001 .

[5]  S..  PROBLEMS OF RELATIVE GROWTH , 2014 .

[6]  K. Pearson.  NOTES ON THE HISTORY OF CORRELATION , 1920 .

[7]  G. Marsaglia.  Evaluating the Normal Distribution , 2004 .

[8]  H. M. Walker.  DE MOIVRE ON THE LAW OF NORMAL PROBABILITY , 2006 .

[9]  C. Read,et al.  Handbook of the Normal Distribution, 2nd Edition. , 1998 .

[10]  H. Hartley,et al.  Recommended Standards for Statistical Symbols and Notation , 1965 .

[11]  T. N. Sriram.  Asymptotics in Statistics–Some Basic Concepts , 2002 .

[12]  E. Lukács,et al.  A Property of the Normal Distribution , 1954 .

[13]  S. Stigler,et al.  The History of Statistics: The Measurement of Uncertainty before 1900 by Stephen M. Stigler (review) , 1986, Technology and Culture.

[14]  Albert J. Kinderman,et al.  Computer Generation of Random Variables Using the Ratio of Uniform Deviates , 1977, TOMS.

[15]  N. L. Johnson,et al.  Continuous Univariate Distributions. , 1995 .

[16]  Stephen M. Stigler,et al.  Mathematical Statistics in the Early States , 1978 .

[17]  Glen McPherson,et al.  Statistics in Scientific Investigation: Its Basis, Application, and Interpretation , 1990 .

[18]  Karl Pearson.  “DAS FEHLERGESETZ UND SEINE VERALLGEMEINER-UNGEN DURCH FECHNER UND PEARSON.” A REJOINDER , 1905 .

[19]  清水 邦夫.  Continuous Univariate Distributions Volume 1/N.L.Johnson,S.Kotz,N.Balakrishnan(1994) , 1995 .

[20]  Stephen M. Stigler.  A Modest Proposal: A New Standard for the Normal , 1982 .

[21]  R. Herrnstein,et al.  The bell curve : intelligence and class structure in American life , 1995 .