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A. Juriˇ<strong>si</strong>ć in V. Batagelj: Verjetnostni račun in statistika 299 ✬ y 0.0 0.2 0.4 0.6 0.8 1.0 ✫ Normalna porazdelitev, n=100 100 150 200 250 x . . . Osnovni izrek statistike Velja pa ˇse več. Vn(x) je stopničasta funkcija, ki se praviloma dobro prilega funkciji F (x). Odstopanje med Vn(x) in F (x) lahko izmerimo s slučajno spremenljivko Dn = sup x∈R Vn(x) − F (x) za n = 1, 2, 3, . . . Zanjo lahko pokaˇzemo osnovni izrek statistike P = 1. lim n→∞ Dn = 0 Torej se z rastjo velikosti vzorca Vn(x) enakomerno vse bolje prilega funkciji F (x) – vse bolje povzema razmere na celotni populaciji. Univerza v Ljubljani ▲ ❙ ▲ ▲ ▲ ● ❙ ▲ ▲ ☛ ✖ ✩ ✪
A. Juriˇ<strong>si</strong>ć in V. Batagelj: Verjetnostni račun in statistika 300 ✬ ✫ Vzorčne ocene Najpogostejˇsa parametra, ki bi ju radi ocenili sta: sredina populacije µ glede na izbrano lastnost – matematično upanje spremenljivke X na populaciji; in povprečni odklon od sredine σ – standardni odklon spremenljivke X na populaciji. Statistike/ocene za te parametre so izračunane iz podatkov z vzorca. Zato jim tudi rečemo vzorčne ocene. 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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