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Slika - Shrani.si

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A. Juriˇ<strong>si</strong>ć in V. Batagelj: Verjetnostni račun in statistika 383<br />

✬<br />

✫<br />

. . . Intervalsko ocenjevanje parametrov<br />

Če pri porazdelitvi X : N(µ, σ) tudi parameter σ ni znan, ga nadomestimo<br />

√<br />

n.<br />

s cenilko S in moramo zato uporabiti Studentovo statistiko T = X−µ<br />

S<br />

Ustrezni interval je tedaj<br />

A = X − t α/2<br />

kjer je P (T > t α/2) = α/2.<br />

S<br />

S<br />

√ , B = X + tα/2 √<br />

n n<br />

Če pa bi ocenjevali parameter σ 2 , uporabimo statistiko χ 2 = (n − 1) S2<br />

σ 2 , ki<br />

je porazdeljena po χ 2 (n − 1). Tedaj sta<br />

A =<br />

(n − 1)S2<br />

b<br />

, B =<br />

(n − 1)S2<br />

a<br />

Konstanti a in b vča<strong>si</strong>h določimo iz pogojev P (χ 2 < a) = α/2<br />

in P (χ 2 > b) = α/2; najkrajˇ<strong>si</strong> interval pa dobimo, ko velja zveza<br />

a 2 p(a) = b 2 p(b) in seveda b<br />

a<br />

p(t)dt = 1 − α.<br />

Univerza v Ljubljani ▲<br />

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▲<br />

● ❙ ▲<br />

▲<br />

☛ ✖<br />

▲<br />

✩<br />

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