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Shneina, Ehfayed.

Extreme values in sequences of independent random variables with mixed distributions

Dozvoljavate umnožavanje, distribuciju i javno saopštavanje dela, i prerade, ako se navede ime autora na način odredjen od strane autora ili davaoca licence, čak i u komercijalne svrhe. Ovo je najslobodnija od svih licenci. Osnovni opis Licence: http://creativecommons.org/licenses/by/3.0/rs/deed.sr_LATN Sadržaj ugovora u celini: http://creativecommons.org/licenses/by/3.0/rs/legalcode.sr-Latn

Academic metadata

Doktorska disertacija

Univerzitet u Beogradu

Matematički fakultet

Other Theses Metadata

Ekstremne vrednosti u nizovima nezavisnih slučajnih veličina sa mešavinama raspodela

[E. Shneina]

V, 68 listova

Mathematics-Probability and Statistics/Matematika-Verovatnoća i Statistika

Datum odbrane: 12.12.2013.

Mladenović, Pavle, 1955- (mentor)

Janković, Slobodanka (član komisije)

Petrović, Ljiljana, 1956- (član komisije)

This thesis has been written under the supervision of my mentor Prof. Dr. Pavle Mladenović at the University of Belgrade, Faculty of Mathematics in the academic year 2012-2013. The title of this thesis is “Extreme values in sequences of independent random variables with mixed distributions”. For good survey of the field, see Resnick, S. I. [25] and Samorodnitsky, Taqqu [27]. The thesis is divided into two chapters. Chapter 1 is divided into 7 sections. In this chapter, we focus on classical results in extreme value theory. We discuss maxima and minima in the first section, univariate extreme value theory in the second section, max-stable distributions in the third section, peaks over threshold models in the fourth section, domain of attraction of the extremal type distributions in the fifth section, tails in the sixth section and tail equivalence in the seventh section.
Chapter 2 is divided into 9 sections. In this chapter, we discuss mixed distributions in the first section, mixture of normal distributions in the second section, mixture of Cauchy distributions in the third section, stable distributions in the fourth section, properties of stable random variables in the fifth section, infinitely divisible distributions in the sixth section. Sections 7 and 8 contain the main results for this dissertation. Mixtures of stable distributions are described in the seventh section and mixtures of an infinite sequence of independent normally distributed variables in the eighth section. Conclusion and future research are in the ninth section.

extreme value theory; mixed distributions; normal distributions; stable distributions

51

English

45534223

Tekst

This thesis has been written under the supervision of my mentor Prof. Dr. Pavle Mladenović at the University of Belgrade, Faculty of Mathematics in the academic year 2012-2013. The title of this thesis is “Extreme values in sequences of independent random variables with mixed distributions”. For good survey of the field, see Resnick, S. I. [25] and Samorodnitsky, Taqqu [27]. The thesis is divided into two chapters. Chapter 1 is divided into 7 sections. In this chapter, we focus on classical results in extreme value theory. We discuss maxima and minima in the first section, univariate extreme value theory in the second section, max-stable distributions in the third section, peaks over threshold models in the fourth section, domain of attraction of the extremal type distributions in the fifth section, tails in the sixth section and tail equivalence in the seventh section.
Chapter 2 is divided into 9 sections. In this chapter, we discuss mixed distributions in the first section, mixture of normal distributions in the second section, mixture of Cauchy distributions in the third section, stable distributions in the fourth section, properties of stable random variables in the fifth section, infinitely divisible distributions in the sixth section. Sections 7 and 8 contain the main results for this dissertation. Mixtures of stable distributions are described in the seventh section and mixtures of an infinite sequence of independent normally distributed variables in the eighth section. Conclusion and future research are in the ninth section.