statsmodels.robust.norms.Hampel.psi#
- Hampel.psi(z)[source]#
The psi function for Hampel’s estimator
The analytic derivative of rho.
- Parameters:
- zarray_like
1d array
- Returns:
- psi
ndarray The value of the psi function.
\[\begin{split}\psi(z) = \begin{cases} z & \text{if } \lvert z \rvert \le a \\ a \cdot \text{sign}(z) & \text{if } a < \lvert z \rvert \le b \\ \frac{a}{c - b} \cdot \text{sign}(z) \cdot (c - \lvert z \rvert) & \text{if } b < \lvert z \rvert \le c \\ 0 & \text{if } \lvert z \rvert > c \\ \end{cases}\end{split}\]
- psi