Second derivative of the Cauchy link function.

        Parameters
        ----------
        p: array-like
            Probabilities

        Returns
        -------
        g''(p) : array
            Value of the second derivative of Cauchy link function at `p`

def deriv2(self, p):
        """
        Second derivative of the Cauchy link function.

        Parameters
        ----------
        p: array-like
            Probabilities

        Returns
        -------
        g''(p) : array
            Value of the second derivative of Cauchy link function at `p`
        """
        a = np.pi * (p - 0.5)
        d2 = 2 * np.pi**2 * np.sin(a) / np.cos(a)**3
        return d2