ASIMETRIČNA WEIBULLOVA PORAZDELITEV IN NJENE UPORABE

Jurić, Višnja (author), Perman, Mihael (mentor), Kozubowski, Tomasz J. (co-mentor)

Disertacija obravnava nesimetrične Weibullove porazdelitve tako v eni kot v več dimenzijah. Predstavimo deloma nove definicije teh porazdelitev in izpeljemo metode za ocenjevanje parametrov, kar je nujna predpostavka za uporabo pri modeliranju finančnih podatkov kot so donosi finančnih naložb ali modeliranje menjalnih tečajev. Po obširnem pregledu v eni dimenziji je predstavljena posplošitev na več dimenzij. Ta posplošitev je dejanski prispevek disertacije. Posplošitev je posredna prek reprezentacij nesimetrične Laplaceove porazdelitve v eni dimenziji. Disertacija navaja lastnosti te nove družine porazdelitev in se loti tudi vprašanj ocenjevanja parametrov in simulacij. Disertacija se zaključi s finančno uporabo te nove družine porazdelitev na dejanskih menjalnih tečajih.

• Language: Slovenian
• Keywords: asimetrična Laplaceova transformacija, dvojna Weibullova porazdelitev, večrazsežna simetrična Weibullova orazdelitev, finančno modeliranje
• Work type: Doctoral dissertation
• Organization: EF - School of Economics and Business
• Year: 2019
• PID: 20.500.12556/RUL-108480
• Publication date in RUL: 04.07.2019

Secondary language

• Language: English
• Title: ASYMMETRIC DOUBLE WEIBULL DISTRIBUTION AND ITS APPLICATIONS

Abstract

The dissertation examines the asymmetric Weibull distributions extended to the higher dimensional setting. Newly developed definitions along with the methods of estimation of the parameters are presented. This provides the basis for applications in modelling financial data including the univariate and the multivariate double Weibull model for currency exchange rates. The dissertation starts with an extensive review of the univariate Weibull distribution followed by its generalization to the multivariate case. This generalization is the core of the dissertation and its main contribution to science. A well known representation of the asymmetric univariate Laplace distribution is used as the starting point. Properties of the new family of distributions are described in detail and parameters are estimated using the method of moments. In the final part of the dissertation an application of the new family of distributions to modelling financial data in the case of bivariate currency exchange rate data set is given. This new family shows the potential for modelling purposes.

• Keywords: asymmetric Laplace law, double Weibull distribution, multivariate asymmetric Weibull distribution, currency exchange rate modelling