Consider two simple random samples $X_1, . . . , X_n $ and $Y_1, . . . , Y_m$, where $X_i ∼ Poisson(µ_x),$ $Y_j ∼ Poisson(µ_y)$, whose elements $X_i$ and $Y_j$ are mutually independent for any indices $i = 1, . . . , n$ and $j = 1, . . . , m$. Regarding the hypotheses $H_0 : µ_x = µ_y$ versus $H_1 : µ_x \neq µ_y$, how to obtain the likelihood ratio test and formulate Pearson's chi-square test? Are these tests asymptotically equivalent?
2026-04-02 19:11:31.1775157091
Likelihood ratio test and formulate Pearson's
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