Function HYPwei transforms vector u as follows \[ HYPwei(u) = \left\{ \begin{array}{cc} 1 & |u| \leq d, \\ \sqrt(A * (k - 1)) * tanh(sqrt((k - 1) * B^2/A)*(c-|u|)/2) .* sign(u)/u & d \leq |u| < c, \\ 0 & |u| \geq c. \\ \end{array} \right. \] where $0 < d < c$ is such that \[ d = \sqrt{[A(k-1)]}\tanh [\frac{1}{2}\sqrt{\frac{(k-1)B^2}{A}}(c - d)], \]

$A$ and $B$ satisfy suitable conditions, and $k$ is related to the bound in the Change of Variance Curve.

More precisely, it is necessary to have $0 < A < B < 2 *normcdf(c)-1- 2*c*normpdf(c) <1$ Remark: hyperbolic psi-function is 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.