For \(\tau>0\), show that the modified transformation \(\mathbb{R}_{+}^{n} ightarrow \mathbb{R}^{n}\)

\[
(g y)_{i}=\dot{y}+\frac{y_{i}^{\lambda}-\dot{y}^{\lambda}}{\lambda \dot{y}^{\lambda-1}}
\]

is continuous at \(\lambda=0\) and satisfies \(g(\tau y)=\tau g(y)\). What are the implications for statistical applications? Show that the Jacobian is

\[
\frac{1}{\lambda}+\frac{\lambda-1}{n \lambda} \dot{y}^{\lambda} \sum y_{i}^{-\lambda} \text {, }
\]

which is positive, and that the limits for \(\lambda ightarrow 0\) and \(\lambda ightarrow 1\) are equal.