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2015 | OriginalPaper | Chapter

7. Multivariate Normal Distribution

Author : Daniel Zelterman

Published in: Applied Multivariate Statistics with R

Publisher: Springer International Publishing

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Abstract

IN THIS CHAPTER, we generalize the bivariate normal distribution from the previous chapter to an arbitrary number of dimensions. We also make use of the matrix notation. The mathematics is generally more dense and relies on the linear algebra notation covered in Chap. 4 In Sect. 4.5 we pointed out there is a limit on what computations we can reasonably perform by hand. For this reason, we illustrate these various operations with the help of R.

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Footnotes
1
Harold Hotelling (1885–1973). US mathematician, statistician, and economist.
 
2
Samuel Stanley Wilks (1906–1964). American mathematician, worked at Princeton University.
 
3
John Wishart (1898–1956). Scottish mathematician and statistician.
 
4
Prasanta Chandra Mahalanobis (1893–1972). Indian scientist and statistician.
 
Literature
go back to reference Mardia KV (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika 57: 519–30. Referenced on page 285. Mardia KV (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika 57: 519–30. Referenced on page 285.
go back to reference Schwager, SJ and Margolin BH (1982). Detection of multivariate normal outliers. Annals of Statistics 10: 943–954. Referenced on page 199. Schwager, SJ and Margolin BH (1982). Detection of multivariate normal outliers. Annals of Statistics 10: 943–954. Referenced on page 199.
go back to reference von Eye A, Bogat GA (2004). Testing the assumption of multivariate normality. Psychology Science 46: 243–258. Referenced on page 199. von Eye A, Bogat GA (2004). Testing the assumption of multivariate normality. Psychology Science 46: 243–258. Referenced on page 199.
go back to reference Wan H, Larsen LJ (2014). U.S. Census Bureau, American Community Survey Reports, ACS-29, Older Americans With a Disability: 2008–2012, U.S. Government Printing Office, Washington, DC, 2014. Referenced on page 205. Wan H, Larsen LJ (2014). U.S. Census Bureau, American Community Survey Reports, ACS-29, Older Americans With a Disability: 2008–2012, U.S. Government Printing Office, Washington, DC, 2014. Referenced on page 205.
Metadata
Title
Multivariate Normal Distribution
Author
Daniel Zelterman
Copyright Year
2015
DOI
https://doi.org/10.1007/978-3-319-14093-3_7

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