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Tukey's Biweight

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TukeysBiweight

The function

psi(x)={x(1-(x^2)/(c^2))^2 for |x|<c; 0 for |x|>c
(1)

sometimes used in robust estimation. It has a minimum at x=-c/sqrt(5) and a maximum at x=c/sqrt(5), where

psi^'(x)=((c-x)(c+x)(c^2-5x^2))/(c^4)=0,
(2)

and inflection points at x=0 and x=+/-c/sqrt(5), where

psi^('')(x)=-(4x(3c^2-5x^2))/(c^4)=0.
(3)

See also

Andrew's Sine

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References

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, p. 697, 1992.

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Tukey's Biweight

Cite this as:

Weisstein, Eric W. "Tukey's Biweight." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TukeysBiweight.html

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