Graf chvostu distribuce bez momentových omezení

• Thesis title in Czech: Graf chvostu distribuce bez momentových omezení
• Thesis title in English: A Tail Plot Without Moment Restrictions
• Key words: Těžké chvosty|Nekonečná střední hodnota|Paretovo rozdělení|Regulérně měnící distribuce|Index chvostu
• English key words: Heavy tails|Infinite mean|Pareto distribution|Regularly varying distribution|Tail index
• Academic year of topic announcement: 2025/2026
• Thesis type: Bachelor's thesis
• Department: Department of Probability and Mathematical Statistics (32-KPMS)
• Supervisor: doc. RNDr. Michal Pešta, Ph.D.
• Author: hidden - assigned and confirmed by the Study Dept.
• Date of registration: 03.09.2025
• Date of assignment: 04.09.2025
• Confirmed by Study dept. on: 04.09.2025

Guidelines

Methods for analyzing probability distributions will be studied with a focus on heavy-tailed data. A new type of mean function will be investigated that can be applied to a wide range of distributions and will allow the identification of special cases such as the Pareto distribution. In contrast to the classical mean excess plot, this approach will make it possible to consider situations where the mean does not exist or where higher moments are infinite. The usefulness of the method will be illustrated through applications to real datasets.

References

[1] Bernhard K (2025) A Pareto Tail Plot Without Moment Restrictions, The American Statistician, 79:2, 156-166, DOI: 10.1080/00031305.2024.2413081
[2] Embrechts P, Klüppelberg C, Mikosch T (1997) Modelling Extremal Events, Berlin: Springer