Multivariate ageing and dependence properties of generalized order statistics and related stochastic models

Positive ageing denotes the adverse effect of age on random life times (survival or failure times) of individuals or units. A positive ageing class contains life time distributions that show a characteristic behavior of positive ageing. Ageing properties are often expressed in terms of the residual life time of units of different ages. The best studied (univariate) ageing class is the IFR (increasing failure rate) class. A life time distribution belongs to this class if the residual life time of a unit of less age dominates the residual life time of a unit of greater age with respect to the stochastic order. Positive dependence describes the tendency of components of a random vector to assume concordant values. Positive dependence notions, like association or the MTP2 notion, measure this tendency. In this thesis, four stochastic models for life time distributions are analyzed with respect to their positive ageing and dependence properties: generalized order statistics, mixture models, order statistics and record values from exchangeable sequences and progressively Type II censored order statistics from INID (independent and not necessarily identically distributed) random variables. Several positive ageing and dependence classes are defined, in particular multivariate IFR, IFRA and NBU classes. There are conditions derived which ensure that vectors of generalized order statistics belong to these multivariate classes. Furthermore, it is examined whether generalized order statistics belong to the (univariate) NBU(2) and NBUC classes. This work contains results concerning the preservation of ageing and dependence properties under mixtures. From these results, it follows that a random vector which is distributed according to an extension of the proportional hazards regression model has the MTP2 property. In addition, the dependence structure of progressively Type II censored order statistics from INID random variables is analyzed. A main result is that vectors of progressively Type II censored order statistics from INID random variables are associated.

Grantor dc:publisher

Publikationsserver der RWTH Aachen University

Year dc:date

2008

Author dc:creator

• Seehafer, Ute

Contributors dc:contributor

• Cramer, Erhard

• info:eu-repo/classification/ddc/510
• Alterung
• stochastische Abhängigkeit
• Mathematik
• Ordnungsstatistiken
• Mischungsmodelle
• Zensierung
• ageing
• dependence
• order statistics
• mixture models
• censoring

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

eng

Identifier

https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-112843%22

OAI record oai:identifier

https://publications.rwth-aachen.de/oai2d?verb=GetRecord&metadataPrefix=oai_dc&identifier=oai%3Apublications.rwth-aachen.de%3A50292