Η διαδικασία Pólya-Lundberg και οι γενικεύσεις της
The Pólya-Lundberg Process and some extensions
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Keywords
Διαδικασία Pólya-Lundberg ; Διαδικασία Delaporte ; Στοχαστική διαδικασία Poisson ; Markov processes ; Στοχαστική διαδικασία άφιξης απαιτήσεωνAbstract
In this thesis we first investigate the Pólya-Lundberg process, which is a special case of
the mixed Poisson process. It is proven that every random variable of a Pólya-Lundberg
process has the negative binomial distribution as its distribution, and that every Pólya-
Lundberg process is a regular Markov process.
We then study the Delaporte process as a generalization of the Pólya-Lundberg process
and we show that its probability distribution is a convolution of a Poisson and a negative
binomial distribution. Another generalization of the Pólya-Lundberg process is the process,
whose every random variable has the generalized negative binomial distribution as
its distribution. This can be induced by a mixed Poisson process with mixing distribution
a generalized negative binomial distribution, as it has been proven by Gerber.
Finally, we study some results of Ruohonen concerning the fitting of the model of a
Delaporte process to several data encountered in the literature, and its comparison with
the Pólya-Lundberg process.
Postgraduate Studies Programme
Αναλογιστική Επιστήμη και Διοικητική ΚινδύνουDepartment
Σχολή Χρηματοοικονομικής και Στατιστικής. Τμήμα Στατιστικής και Ασφαλιστικής ΕπιστήμηςNumber of pages
119Language
GreekCollections
Except where otherwise noted, this item's license is described as
Attribution-NonCommercial-NoDerivatives 4.0 Διεθνές
Attribution-NonCommercial-NoDerivatives 4.0 Διεθνές