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Competitive Stats
Q46Section I (Objective (Q1–Q80))46 of 80

Method of moments estimator — Gamma

Let x1,x2,…,xnx_1,x_2,\dots,x_n be a random sample from a distribution with probability density function

f(x;α)=1Γ(α)xα−1e−x;0≤x<∞,α>0.f(x;\alpha)=\frac1{\Gamma(\alpha)}x^{\alpha-1}e^{-x};\qquad 0\le x<\infty, \alpha>0.

Then the estimator of α\alpha obtained by method of moments is:

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