20.500.12556/RUL-162180 Intervali zaupanja za ocenjevanje binomskega deleža Confidence intervals for the estimation of the binomial proportion Delo obravnava problematiko izražanja natančnega intervala zaupanja pri ocenjevanju deleža. Asimpotični Waldov interval je pri majhnih vzorcih za praktično uporabo preveč nenatančen, zato predstavimo tri alternativne konstrukcije: Wilsonov, Agresti--Coullov in Clopper--Pearsonov. Ker točen interval za binomsko porazdelitev ne obstaja, lahko uporabljamo konservativnega. Pokazali bomo, da je Clopper--Pearsonov interval konservativen in ga izrazili s pomočjo kvantilov porazdelitve beta. Ker so dejanske stopnje tveganja Clopper--Pearsonovega intervala v povprečju dosti nižje od predpisanih, bomo predstavili še dva, ki sicer ne dosegata nominalne stopnje pokritosti, a sta ji v povprečju bližje kot Waldov ali Clopper--Pearsonov interval. V drugem delu bomo z računalniškim programom vizualno primerjali intervale pri različnih stopnjah zaupanja. Primerjali bomo dejanske stopnje pokritosti z navedeno pri različnih dejanskih vrednostih deleža. Opazovali bomo vpliv zaokroževanja mej na pokritost intervalov in predstavili, na koliko mest je potrebno zaokrožiti Waldov interval, da si zagotovimo povprečno nominalno pokritost, in na koliko mest Agresti--Coullovega, da bo konservativen. The work deals with the problematic of precisely expressing confidence intervals for proportion estimation. The asymptotic Wald interval is practically useless for small sample sizes, so we provide three alternative constructions: the Wald, Agresti--Coull and Clopper--Pearson intervals. Since an exact confidence interval does not exist for the binomial distribution, we can have at most a conservative one. We show that the Clopper--Pearson interval is conservative and express it in terms of quantiles of the beta distribution. The Clopper--Pearson interval is, on average, a lot more conservative than desired, so we suggest two alternative intervals that technically do not achieve the desired coverage, but are on average a lot closer to it than Wald or Clopper--Pearson. In the second part, we compare intervals visually by graphing them with a computer program at various confidence levels. We compare nominal to actual coverage levels of each interval at different values of the proportion. We observe the influence of rounding errors on the coverage probability, and calculate the number of decimal places to which we must round the Wald interval to achieve mean nominal coverage, and the Agresti--Coull interval to achieve conservative coverage. interval zaupanja Wald Wilson Agresti-Coull Clopper-Pearson confidence interval Wald Wilson Agresti-Coull Clopper-Pearson true false false Slovenski jezik Angleški jezik Diplomsko delo/naloga 2024-09-19 12:20:08 2024-09-19 12:20:15 2024-11-08 05:06:06 0000-00-00 00:00:00 2024 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 37556 214135555 Ploj_Yon_-_Intervali_zaupanja_za_ocenjevanje_binomskega_deleza.pdf Ploj_Yon_-_Intervali_zaupanja_za_ocenjevanje_binomskega_deleza.pdf 1 C0AAC500F6D25788AE9C444BA4447010 f588eac6472a7fb145ea4beddb69e2ec4e00dcc6a61ba35f01f18abada722837 a6ff4c5c-7670-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=191352 Fakulteta za računalništvo in informatiko 0 0 0