Abstract
In this chapter, we introduce the ‘multivariate generalized Polya process (MVGPP)’ recently developed in the literature and discuss its properties. Initially, we define and study bivariate generalized Polya process and briefly discuss the corresponding reliability application. The bivariate generalized Polya process is extended to the multivariate case. We define a new dependence concept for multivariate point processes and, based on it, we analyze the dependence structure of the multivariate generalized Polya process.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Allen F, Gale D (2000) Financial contagion. J Polit Econ 108:1–34
Aven T, Jensen U (1999) Stochastic models in reliability. Springer, New York
Aven T, Jensen U (2000) A general minimal repair model. J Appl Probab 37:187–197
Bowsher CG (2006) Modelling security market events in continuous time: intensity based, multivariate point process models. J Econometrics 141:876–912
Cha JH (2014) Characterization of the generalized Polya process and its applications. Adv Appl Probab 46:1148–1171
Cha JH, Giorgio M (2016) On a class of multivariate counting processes. Adv Appl Probab 48:443–462
Cox DR, Lewis PAW (1972) Multivariate point processes. In: LeCam LM (ed) Proceedings of the sixth Berkeley symposium in mathematical statistics, pp 401–448
Cuadras CM (2002) On the covariance between functions. J Multivar Anal 81:19–27
Daley DJ (1968) The correlation structure of the output process of some single server queueing systems. Ann Math Stat 39:1007–1019
Finkelstein M, Cha JH (2013) Stochastic modelling for reliability: shocks, burn-in and heterogeneous populations. Springer, London
Joe H (1997) Multivariate models and dependence concepts. Chapman and Hall, London
Lehmann EL (1966) Some concepts of dependence. Ann Math Stat 37:1137–1153
Partrat C (1994) Compound model for two dependent kinds of claims. Insur Math Econ 15:219–231
Shaked M, Shanthikumar JG (2007) Stochastic orders. Springer, New York
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Cha, J.H., Finkelstein, M. (2018). Multivariate Generalized Polya Process. In: Point Processes for Reliability Analysis. Springer Series in Reliability Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-73540-5_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-73540-5_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-73539-9
Online ISBN: 978-3-319-73540-5
eBook Packages: EngineeringEngineering (R0)