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2015 | OriginalPaper | Chapter

5. The Univariate Normal Distribution

Author : Daniel Zelterman

Published in: Applied Multivariate Statistics with R

Publisher: Springer International Publishing

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Abstract

HE NORMAL DISTRIBUTION is central to much of statistics. In this chapter and the two following, we develop the normal model from the univariate, bivariate, and then, finally, the more general distribution with an arbitrary number of dimensions.

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Footnotes
1
Abraham de Moivre (1667–1754). French mathematician and probabilist.
 
2
Carl Friedrich Gauss (1777–1855). German mathematician and physicist.
 
3
Augustin-Louis Cauchy 1789–1857. French mathematician.
 
4
Karl Pearson (1857–1936). British historian, lawyer, and mathematician.
 
5
There is mathematical theory to suggest that n 4∕5 is about the correct number of categories needed when drawing a histogram. See Tapia and Thompson (1978, p. 53) for details on this.
 
6
Andrey Nikolaevich Kolmogorov (1903–1987). Soviet mathematician and probabilist.
 
7
Nikolai Vasil’evich Smirnov (1900–  ). Soviet probabilist.
 
8
Samuel Sanford Shapiro (1930– ). American statistician and engineer.
 
9
Martin Bradbury Wilk (1922–2013). Canadian statistician and former Chief Statistician of Canada.
 
10
William Sealy Gosset (1876–1937). British mathematician
 
11
Bernard Lewis Welch (1911–1989). English statistician.
 
12
Siméon Denis Poisson (1781–1840). French mathematician and physicist.
 
Literature
go back to reference Box GEP and Cox DR (1964). An analysis of transformations (with discussions) Journal of the Royal Statistical Society (B) 26: 211-52. Referenced on pages 123 and 123. Box GEP and Cox DR (1964). An analysis of transformations (with discussions) Journal of the Royal Statistical Society (B) 26: 211-52. Referenced on pages 123 and 123.
go back to reference Jarque CM and Bera AK (1987). A test for normality of observations and regression residuals. International Statistical Review 55: 163–172. JSTOR 1403192. Referenced on page 128. Jarque CM and Bera AK (1987). A test for normality of observations and regression residuals. International Statistical Review 55: 163–172. JSTOR 1403192. Referenced on page 128.
go back to reference Shapiro SS, Wilk MB (1965). An analysis of variance test for normality (complete samples). Biometrika 52 (3–4): 591–611. doi:10.1093/biomet/52.3-4.591. JSTOR 2333709 MR205384. Referenced on pages 130 and 199. Shapiro SS, Wilk MB (1965). An analysis of variance test for normality (complete samples). Biometrika 52 (3–4): 591–611. doi:10.​1093/​biomet/​52.​3-4.​591. JSTOR 2333709 MR205384. Referenced on pages 130 and 199.
go back to reference Sullivan M (2008). Statistics: Informed Decisions Using Data, Third Edition. Pearson. Referenced on page 135. Sullivan M (2008). Statistics: Informed Decisions Using Data, Third Edition. Pearson. Referenced on page 135.
go back to reference Tapia RA and Thompson JR (1978). Nonparametric Probability Density Estimation. Baltimore: Johns Hopkins University Press. Referenced on page 127. Tapia RA and Thompson JR (1978). Nonparametric Probability Density Estimation. Baltimore: Johns Hopkins University Press. Referenced on page 127.
Metadata
Title
The Univariate Normal Distribution
Author
Daniel Zelterman
Copyright Year
2015
DOI
https://doi.org/10.1007/978-3-319-14093-3_5

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