wilson.hilferty: Wilson-Hilferty transformation

Description Usage Arguments Details References See Also Examples

View source: R/wilson_hilferty.R

Description

Returns the Wilson-Hilferty transformation of random variables with chi-squared distribution.

Usage

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Arguments

x

vector or matrix of data with, say, p columns.

Details

Let F = D^2/p be a random variable, where D^2 denotes the squared Mahalanobis distance defined as

D^2 = (\bold{x} - \bold{μ})^T \bold{Σ}^{-1} (\bold{x} - \bold{μ})

Thus the Wilson-Hilferty transformation is given by

z = \frac{F^{1/3} - (1 - \frac{2}{9p})}{(\frac{2}{9p})^{1/2}}

and z is approximately distributed as a standard normal distribution. This is useful, for instance, in the construction of QQ-plots.

References

Wilson, E.B., and Hilferty, M.M. (1931). The distribution of chi-square. Proceedings of the National Academy of Sciences of the United States of America 17, 684-688.

See Also

cov, Mahalanobis

Examples

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x <- iris[,1:4]
z <- wilson.hilferty(x)
par(pty = "s")
qqnorm(z, main = "Transformed distances Q-Q plot")
abline(c(0,1), col = "red", lwd = 2, lty = 2)

fastmatrix documentation built on Oct. 18, 2021, 5:08 p.m.