Let $X=(X_1,\ldots,X_n)$, with $X_1,\ldots,X_n$ iid and $X_i$ with cts distribution having pdf,

\begin{align} g_\lambda (y) &= \begin{cases} \lambda y^{-2}, & y \geq \lambda\\ 0, & \text{else} \end{cases} \end{align} where $\lambda >0$

We are asked to find the ML estimate of $\lambda$

I have \begin{align} L &= \prod_{i=1}^n g_\lambda (x_i) = \lambda^n \prod_{i=1}^n x_i^{-2} \end{align} for the likelihood function but I'm stuck on how to find the MLE.

All I've really noticed is that $L \neq 0$ when $\min\{x_i,\ldots,x_n\}\geq \lambda$ and my first attempt says that the MLE for $\lambda$ is infinite.


marked as duplicate by StubbornAtom, Community Sep 17 at 15:09

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