For which values of (alpha) is the transformation [ g_{alpha}(x)=frac{(-log (1-x))^{alpha}}{alpha}-frac{(-log (x))^{alpha}}{alpha} ] differentiable and strictly monotone

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For which values of $\alpha$ is the transformation

\[
g_{\alpha}(x)=\frac{(-\log (1-x))^{\alpha}}{\alpha}-\frac{(-\log (x))^{\alpha}}{\alpha}
\]

differentiable and strictly monotone $(0,1) ightarrow \mathbb{R}$ ?

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Ten Projects In Applied Statistics

ISBN: 9783031142741

1st Edition

Authors: Peter McCullagh

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Question Posted: Feb 04, 2024 02:00 AM

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For which values of (alpha) is the transformation [ g_{alpha}(x)=frac{(-log (1-x))^{alpha}}{alpha}-frac{(-log (x))^{alpha}}{alpha} ] differentiable and strictly monotone

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Ten Projects In Applied Statistics

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