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Q47Section I (Objective (Q1–Q80))47 of 80

Statistical Inference — method of moments estimator of gamma shape

What is the estimator of α\alpha obtained by method of moments for f(x∣α,β)=e−xβxα−1βαΓ(α)f(x|\alpha,\beta) = \frac{e^{-\frac{x}{\beta}}x^{\alpha-1}}{\beta^\alpha\Gamma(\alpha)}; x>0x > 0, α>1\alpha > 1, β>0\beta > 0?

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