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Berkeley
STAT 135 -
METHOD OF MOMENTS
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METHOD OF MOMENTSA simple three step procedure. Let’s cover a few examples.Example Y1, . . . , Ynare iid U(0, θ)1. Moment: E(Y1) =2. Solve for θ =3. Substitute:ˆθ =Example Z1, . . . , Znare iid N(µ, σ2)1. Moment: E(Z1) =2. Solve for µ =3. Substitute: ˆµ =Example U1, . . . , Unare iid Gamma(2, λ)1. Moment: E(U1) =2. Solve for λ =3. Substitute:ˆλ =1Example X1, . . . , Xnare iid Gamma(α, λ)1. 2 Moments: E(X1) =E(X21) =2. Solve for α = andλ =3. Substitute: ˆα =ˆλ =Alternative MOM for the case where X1, . . . , Xnare iid P oisson(λ)1. 2ndMoment: E(X21) =2. Solve for λ =3. Substitute:ˆλ
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