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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Notes
- 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.
References
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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.
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.
Sullivan M (2008). Statistics: Informed Decisions Using Data, Third Edition. Pearson. Referenced on page 135.
Tapia RA and Thompson JR (1978). Nonparametric Probability Density Estimation. Baltimore: Johns Hopkins University Press. Referenced on page 127.
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Zelterman, D. (2015). The Univariate Normal Distribution. In: Applied Multivariate Statistics with R. Statistics for Biology and Health. Springer, Cham. https://doi.org/10.1007/978-3-319-14093-3_5
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