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Abstract:
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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. |