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Abstract
In this thesis, we present three different topics of research which are related to the theory of phasetype distributions. Those topics are explained next. The ﬁrst research work is on order statistics from matrixgeometric distributions in the case of a sample of independent and nonidentically distributed random variables. We prove that order statistics from matrixgeometric distributions are matrixgeometric distributed and we provide representations for their distributions. The second research work is a study of the discrete version of multivariate phasetype distributions introduced by V. G. Kulkarni. We give an expression for the joint probabilitygenerating function in the similar way than in the continuous time case and under this base we make an analysis of this class of distributions and present examples that are commonly found in the literature. The third research work presented came out with the aim of relating the last two topics. That is, we found a problem which relates the concept of order statistics and multivariate phasetype distributions introduced by V. G. Kulkarni, the last in the case of continuous time. Thus, we present a research on concomitants of phasetype distributions. We provide a procedure to calculate the density function of concomitants of phasetype distributions and we prove that concomitants of phasetype distributions are phasetype distributed.
Original language  English 

Publisher  DTU Compute 

Number of pages  177 
Publication status  Published  2019 
Series  DTU Compute PHD2018 

Volume  492 
ISSN  09093192 
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Dive into the research topics of 'Order statistics and multivariate discrete phasetype distributions.'. Together they form a unique fingerprint.Projects
 1 Finished

Risk assessment woth matrixanalytic methods
Campillo Navarro, A., Nielsen, B. F., Bladt, M., Stockmarr, A., Hobolth, A. & Lillo, R. E.
Technical University of Denmark
15/07/2015 → 13/03/2019
Project: PhD