Gaussian distribution is the most applied in practice and because of that reason there is a great amount of studies done in this area. In this report we look at Gaussian distribution from a point of view of extreme value theory. More concretely, moments of maximum of normally distributed values are discussed.
There are methods to calculate moments of extremes of independent identically distributed normal values, values with different variances and asymptotical results.
In this work a case of dependant variables is analyzed and aim is to look for results in similar cases that is done for independent variables. Continuing Bachelor’s work formula for moment calculation of maximum of two dependent normal variables with all different parameters is presented. Also there is a proof of formula for calculation of odd order moments of three dependent variable maximum. This result is generalized for random variable vectors of any length. There is a theorem stated, according to which moments of length n vector maximum could be expressed by same order moments of shorter vectors. Unfortunately, because of requirements for numbers n and m, no recursion method could be applied.
Using computer, maximum of various length random vectors with dependent components is simulated and average is analyzed. In experiments relation between mean values of dependent and independent variable maximums is observed. This relation is stated in a form of a formula and proved for vectors of any length. In this... [to full text]
| Identifer | oai:union.ndltd.org:LABT_ETD/oai:elaba.lt:LT-eLABa-0001:E.02~2005~D_20050609_121407-66272 |
| Date | 09 June 2005 |
| Creators | Burauskaitė, Agnė |
| Contributors | Saulis, Leonas, Rudzkis, Rimantas, Janilionis, Vytautas, Barauskas, Arūnas, Aksomaitis, Algimantas, Navickas, Zenonas, Pekarskas, Vidmantas, Bloznelis, Mindaugas, Valakevičius, Eimutis, Kaunas University of Technology |
| Publisher | Lithuanian Academic Libraries Network (LABT), Kaunas University of Technology |
| Source Sets | Lithuanian ETD submission system |
| Language | Lithuanian |
| Detected Language | English |
| Type | Master thesis |
| Format | application/pdf |
| Source | http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2005~D_20050609_121407-66272 |
| Rights | Unrestricted |
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