Скачать или смотреть Poisson LRT | Neyman-Pearson vs UMP/UMPU | UPSC ISS 2023 Paper-2 | Problem - 29 Part-2 | RitwikMath

**UPSC ISS hypothesis testing theory**! \(X_i \sim Poisson(λ 0)\)

**Poisson KEY PROPERTIES**:
*One-parameter exponential family*
**Complete sufficient statistic**: T = ΣX_i
*Monotone Likelihood Ratio (MLR)* in T

**Likelihood Ratio Test (LRT) Analysis**:
*✓ LRT = Neyman-Pearson test* (simple H₀ vs H₁)
*✓ LRT = UMP test* (one-sided: H₀:λ=λ₀ vs H₁:λ λ₀)
*✓ LRT statistic is function of T* (sufficiency)

**Exponential Family Magic**: MLR + Completeness → **LRT gives optimal tests**!

*Answer**: All statements about **LRT equivalence* are correct!


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