20.500.12556/RUL-150802 Steinova lema delo diplomskega seminarja Stein's lemma Steinova lema je čudovit in hkrati preprost rezultat teorije verjetnosti in statistike, v osnovi razvit na normalni porazdelitvi za eno- in večdimenzionalne slučajne vektorje, na podlagi katerih neposredno povezuje enakost v enačbi z normalnostjo njihove porazdelitve. Obenem predstavlja tudi uporabno orodje za določanje sestave portfelja v poslovnih financah in osnovni gradnik Steinove metode za ocenjevanje napake pri aproksimaciji porazdelitev slučajnih vektorjev. Osrednja naloga tega dela je predstaviti Steinovo lemo za poljuben normalni slučajni vektor, interpretirati njen pomen in spoznati nekaj njenih alternativnih praktičnih zapisov. V nadaljevanju pa, s ciljem dokazati centralni limitni izrek na vsoti neodvisnih enako porazdeljenih slučajnih spremenljivk, sledi še predstavitev Steinove metode. Stein's lemma is a beautiful and, at the same time, straightforward result in probability theory and statistics. Primarily developed based on the normal distribution for one- and multidimensional random vectors, directly connecting the equality in the equation with the normality of their distributions. Additionally, it serves as a useful tool for determining portfolio composition in business finance and is a fundamental building block of Stein's method for estimating the error in approximating distributions of random vectors. The central task of this work is to present Stein's lemma for any normal random vector, interpret its significance, and explore some of its alternative practical formulations. Furthermore, with the aim of proving the central limit theorem for the sum of independent identically distributed random variables, a presentation of Stein's method follows. Stein Steinova lema Steinova metoda Normalna porazdelitev Stein Stein's lemma Stein's method Normal distribution true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2023-09-23 08:15:04 2023-09-23 08:15:08 2024-05-29 09:53:34 0000-00-00 00:00:00 2023 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.2 136699 165546243 10409.pdf 10409.pdf 1 4FFD370CED5E091A2D420DD8B8CDDC2D 42ca1f51b2b3fe9d6d9ffadc4f24746a0793c49e27a2dcadb1a8c4dabe2e9a13 8b9cc580-59d8-11ee-b87d-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=175616 Fakulteta za matematiko in fiziko 0 0 0