Tukey's Biweight

Author

Eric W. Weisstein
May 15, 2003

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Statistics/TukeysBiweight.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/TukeysBiweight.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Definition

ψ[x_,c_]:=x(((1-((x^2)/(c^2))))^2)(UnitStep[x+c ]-UnitStep[x-c])

Plot

<<Graphics`Colors`;

Plot[ψ[x,1],{x,-1.5,1.5},PlotStyle->Red,Ticks->None,AxesLabel->TraditionalForm/@{x,HoldForm[ψ[x]]}]

Extrema

Factor[Simplify[D[ψ[x,c],x]]]

Solve[(c^2)-5 (x^2)==0,x]

Inflection

Factor[Simplify[D[ψ[x,c],{x,2}]]]

Solve[(c^2)-5 (x^2)==0,x]