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Luận văn toán học EXTREME VALUES AND PROBABILITY DISTRIBUTION FUNCTONS ON FINITE DIMENSIONAL SPACES

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Luận văn toán học EXTREME VALUES AND PROBABILITY DISTRIBUTION FUNCTONS ON FINITE DIMENSIONAL SPACES

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. VIETNAM NATIONAL UNIVERSITY UNIVERSITY OF SCIENCE FACULTY OF MATHEMATICS, MECHANICS AND INFORMATICS Do Dai Chi EXTREME VALUES AND PROBABILITY DISTRIBUTION FUNCTONS ON FINITE DIMENSIONAL SPACES Undergraduate. 2012 VIETNAM NATIONAL UNIVERSITY UNIVERSITY OF SCIENCE FACULTY OF MATHEMATICS, MECHANICS AND INFORMATICS Do Dai Chi EXTREME VALUES AND PROBABILITY DISTRIBUTION FUNCTONS ON FINITE DIMENSIONAL SPACES Undergraduate. a standard exponential distribution. Then the distribution function of X is given by F X (x) = 1 −e −x , x > 0. If X 1 , X 2 , . . . are i.i.d. random variables with common distribution function

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Mục lục

  • Acknowledgments

  • List of abbreviations and symbols

  • Introduction

  • Univariate Extreme Value Theory

    • Introduction

      • Limit Probabilities for Maxima

      • Maximum Domains of Attraction

        • Max-Stable Distributions

        • Extremal Value Distributions

          • Extremal Types Theorem

          • Generalized Extreme Value Distributions

          • Domain of Attraction Condition

            • General Theory of Domains of Attraction

            • Condition for belonging to Extreme Value Domain

            • Multivariate Extreme Value Theory

              • Introduction

              • Limit Distributions of Multivariate Maxima

                • Max-infinitely Divisible Distributions

                • Characterizing Max-id Distributions

                • Multivariate Domain of Attraction

                  • Max-stability

                  • Basic Properties of Multivariate Extreme Value Distributions

                  • Standardization

                  • Conclusion

                  • Appendix

                    • Modes of Convergence

                    • Inverses of Monotone Functions

                    • Some Convergence Theorems

                    • Bibliography

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