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Tagged with neyman-pearson-lemma uniform-distribution
3 questions
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Prove that a test is most powerful when $X_1,\cdots,X_n\sim U(0,\theta)$
Let $X_1,\cdots,X_n\sim U(0,\theta),\theta >0$ be independent random variables. I want to prove that $\phi :\mathbb{R}^n\to [0,1]$ given by $\phi (x):=\begin{cases}1,&\theta _0<x_{(n)}\vee ...
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How to Justify this Two-Sided Test is UMP with NP Lemma?
UMP tests generally do not exist for two sided tests, ie $H_0: \theta = \theta_0$ vs $H_a: \theta \neq \theta_0$. However, if we observe $n$ iid observations of $X\sim Unif(0,\theta)$, we can ...
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Finding UMPT for uniform distribution with varying support
$\textbf{Problem}$ Let $X_1,\dots,X_n$ be a random sample from $f(x;\theta) = 1 / \theta$, where $0 < x < \theta$. We want to test $H_0: \theta \leq \theta_0$ versus $H_1: \theta > \theta_0$. ...
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