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A. Juriˇ<strong>si</strong>ć in V. Batagelj: Verjetnostni račun in statistika 349 ✬ ✫ . . . Učinkovitost cenilk Torej velja v Rao-Cramérjevi oceni enakost natanko takrat, ko je ∂ ln L ∂ζ = A(ζ)(C − ζ) kjer je A(ζ) konstanta, odvisna od ζ in neodvisna od vzorca. Zato je tudi oziroma končno (DC) −1 ∂ ln L = E( ∂ζ )2 = A(ζ) 2 E(C − ζ) 2 = A(ζ) 2 DC DC = |A(ζ)| −1 Univerza v Ljubljani ▲ ❙ ▲ ▲ ▲ ● ❙ ▲ ▲ ☛ ✖ ✩ ✪
A. Juriˇ<strong>si</strong>ć in V. Batagelj: Verjetnostni račun in statistika 350 ✬ Najučinkovitejˇse cenilke za parametre normalne porazdelitve Naj bo X : N(µ, σ). Tedaj je in ter dalje ln L = ln L = 1 (2π) n/2σn e−(( X1−µ σ 1 (2π) n/2σn − ((X1 − µ σ ∂ ln L ∂µ = X1 − µ σ2 + · · · + Xn − µ σ 2 ) 2 +···+( Xn−µ σ ) 2 )/2 ) 2 + · · · + ( Xn − µ ) σ 2 )/2 n = (X − µ) σ2 Torej je vzorčno povprečje X najučinkovitejˇsa cenilka za µ z disperzijo DX = ✫ σ2 n . Univerza v Ljubljani ▲ ❙ ▲ ▲ ● ❙ ▲ ▲ ☛ ✖ ▲ ✩ ✪
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✬ ✫ Ljubljana, 6. oktober 2008
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A. Juriˇsić in V. Batagelj: Verje
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