Η διαδικασία Pólya-Lundberg και οι γενικεύσεις της
The Pólya-Lundberg Process and some extensions
KeywordsΔιαδικασία Pólya-Lundberg ; Διαδικασία Delaporte ; Στοχαστική διαδικασία Poisson ; Markov processes ; Στοχαστική διαδικασία άφιξης απαιτήσεων
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.