Function TBpsider transforms vector x as follows $$TBpsider(x)= \left\{ \begin{array}{cc} 1- (x/c)^2 [6- 5 (x/c)^2] & \mbox{if} |x/c|<=1 \\ 0 & \mbox{if} |x/c|>1 \\ \end{array} \right.$$

Remark: Tukey's biweight psi-function is almost linear around $u = 0$ in accordance with Winsor's principle that all distributions are normal in the middle.

This means that $\psi (u)/u$ is approximately constant over the linear region of $\psi$, so the points in that region tend to get equal weight.