Μοντέλα πιθανοτήτων για περιγραφή μη κανονικών κινδύνων
Probability models for fitting non-normal data
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Keywords
Προσομοίωση ; Μοντέλα πιθανοτήτων ; Μη κανονικά δεδομένα ; Γενικευμένη μετασχηματισμένη κατανομή ; Νέα κατανομή με βαριά ουρά ; Non normal data ; Fitting ; Simulation ; Generalised transmuted distribution ; New heavy tailed distribution ; Εκθετικοποιημένη κατανομή ; Exponential distributionAbstract
In the fields of economics, insurance science and risk management, it is quite often to deal with data that cannot be fully described by the classical distributions; such data include the lifetime of patients participating in clinical trials or the loss resulting from non-performing loans of a bank. In the recent years many researchers have focused on finding new distribution models with greater flexibility and better fitting to this kind of data.
This thesis will present two new classes of distributions, the techniques used to develop them as well as their main properties. More specifically, we will present the generalized transmuted class of distributions (GT-F) and a new heavy tailed class of distributions (NHT-F) which extend some classical distributions. The latter ones take the role of the generator in the new models.
The first chapter introduces the topic of the present thesis.
The second chapter includes an introductory section which presents basic concepts from the fields of probabilities and statistics to which references are made throughout the thesis.
The third chapter refers to the generalized transmuted class of distributions with generator a distribution F. The definition of the class and its basic properties are presented, along with techniques for estimating its parameters.
In Chapter 4, two cases of the generalized transmuted class of distributions are studied, one with the exponential distribution as generator and a second one with the gamma distribution as generator.
The fifth chapter presents the second class of distributions studied in this thesis, a new heavy tailed class of distributions with generator a distribution F. Its definition and basic properties are presented, along with techniques for estimating its parameters.
In the sixth chapter, two cases of the new heavy tailed class of distributions are studied, when the exponential and the gamma distribution take the role of the generator.
The seventh chapter examines the fitting of the new models analyzed in chapters four and six to real data.
Finally, the annex provides definitions of various concepts that have been mentioned in the main body of this thesis, relevant proofs and the codes used.
Postgraduate Studies Programme
Αναλογιστική Επιστήμη και Διοικητική ΚινδύνουDepartment
Σχολή Χρηματοοικονομικής και Στατιστικής. Τμήμα Στατιστικής και Ασφαλιστικής ΕπιστήμηςNumber of pages
154Language
GreekCollections
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Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα
Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα