20.500.12556/DKUM-79211 Merjenje in testiranje multivariatnih razdalj Measuring and testing multivariate distances Statistika kot interdisciplinarna veja matematike obsega številne uporabne metode preučevanja različnih spremenljivk na podlagi realnih, življenjskih primerov. Prednost statističnih metod je predvsem vključenost številnih preiskovanih spremenljivk. Metode preiskovanja so povezane tudi z ostalimi matematičnimi disciplinami, kot so algebra, analiza in geometrija. Osrednji in največkrat uporabljeni pojem je razdalja. Vrednosti razdalje dobimo s pomočjo osnovnih statistik, prikazujemo pa jih z matrikami in v tabelah. Magistrsko delo je razdeljeno na dva dela. V prvem delu smo opredelili osnovne statistične pojme, uporabnost matrik v statistiki ter osnovne pojme metrike in norme, ki so osnova osrednjega dela naloge. Pojasnili smo osnovne statistike, kot so disperzija, aritmetična sredina, varianca in kovarianca, ter jih podkrepili z zgledi. Prav tako smo opredelili in z zgledi pojasnili pojma metrika in norma ter natančneje matrike in vrste metrik glede na statistične osnovne pojme. V drugem delu smo osnovne pojme matematičnih disciplin povezali z zgledi različnih znanih razdalj, s čimer smo pridobili boljši vpogled v interdisciplinarnost statistike. Statistics is as an interdisciplinary branch of mathematics which encompasses useful methods of studying various variables based on real-life examples. The main advantage of statistical methods is the inclusion of many investigated variables. Investigation methods are also related to other mathematical disciplines such as algebra, analysis and geometry. The central and most used term is distance. Distance values are calculated with the basic statistics, and they are shown with matrices and in tables. The master's thesis is composed of two parts. In the first part, we defined the basic statistical concepts and the applicability of matrices in statistics. In addition, we presented basic concepts of metrics and norms, which were the basis of the central part of our thesis. We defined basic statistics such as variance, arithmetic mean, variance, and covariance, and illustrated them with examples. We also defined and explained the concepts of metrics and norm, more precisely matrices and types of metrics according to statistical basic concepts. In the second part of our thesis, we connected the basic concepts of mathematics with examples of various types of distances, thus gaining a better insight into the interdisciplinarity of statistical science. statistika multivariatna razdalja Mahalanobisova razdalja evklidska razdalja Penrosova razdalja. statistics multivariate distance Mahalanobis distance Euclidean distance Penrose distance. true true false [L. Gračner] Slovenski jezik Angleški jezik Magistrsko delo/naloga 2021-05-26 09:40:45 2021-08-03 09:26:46 2022-08-09 20:17:13 0000-00-00 00:00:00 2021 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.237(043.2) 70565635 MAG_Gracner_Lucija_2021.pdf MAG_Gracner_Lucija_2021.pdf 1 13A7078B4D8078778C95835F7E926853 acb1af495feb68236fbd1f02ad03ba12c69ff8d2bc733123979aae333cbb682b f4a93a45-bdf6-11eb-b1be-00155d581298 20.500.12556/dkum/89eb9a9b-8454-4698-b9d4-6d29d389ee58 https://dk.um.si/Dokument.php?lang=slv&id=150388 Fakulteta za naravoslovje in matematiko 0 0 0