statsmodels.robust.norms.Hampel.rho#
- Hampel.rho(z)[source]#
The robust criterion function for Hampel’s estimator
- Parameters:
- zarray_like
1d array
- Returns:
- rho
ndarray The value of the robust criterion function.
\[\begin{split}\rho(z) = \begin{cases} \frac{z^2}{2} & \text{if } \lvert z \rvert \le a \\ a \lvert z \rvert - \frac{a^2}{2} & \text{if } a < \lvert z \rvert \le b \\ \frac{a}{2}(b + c - a) - \frac{a}{2(c - b)}(c - \lvert z \rvert)^2 & \text{if } b < \lvert z \rvert \le c \\ \frac{a}{2} \cdot (b + c - a) & \text{if } \lvert z \rvert > c \end{cases}\end{split}\]
- rho