Let xi i 1 2 be independent observations from the gamma, Basic Statistics

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Let xi i 1 2 be independent observations from the gamma

Let X_i, i = 1, 2, be independent observations from the gamma distributions Γ(a, γ₁) and Γ(a, γ₂), respectively, where a > 0 is known and γ_i > 0, i = 1, 2, are unknown. Find the Bayes factor and the Bayes test for H₀; γ₁ = γ₂ versus H₁; γ₁ ≠ γ₂under the prior c.d.f. Π = π₀Π₀ + (1 - π₀)Π₁, where Π₀(x₁, x₂) = G(min{x₁, x₂}), Π₁(x₁, x₂) = G(x₁)G(x₂), G(x) is the c.d.f. of a known gamma distribution, and π₀ is a known constant.

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Basic Statistics: Let xi i 1 2 be independent observations from the gamma

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