New answers tagged logarithm
9
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Distribution of $Y=-\log(X)$ when $X\sim \operatorname{Beta}(\alpha,\beta)$
The moment-generating function of $Y=-\ln X$ is by definition
\begin{align}
M(t)&=E(e^{-t\ln X})\\&=E(X^{-t})\\&=\frac{\Gamma(\alpha+\beta)}{\Gamma(\alpha)\Gamma(\beta)}\int_0^1 x^{\alpha-...
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