General Multivariate Weibull Processes

Abstract

Two multivariate stationary processes with general multivariate Weibull marginals are developed and studied. The joint distribution of the two adjacent events in the processes and the distributions of the finite sample minima as well as the geometric minima are derived. The characterization properties of these two processes are also proved.

Keywords:

• Autoregressive GMW-AR(1) process
• Characterizations
• General multivariate Weibull distribution
• GMW
• Level upcrossings
• Minification process
• Moving-average GMW-MA(q) process
• Stationary

Mathematics Subject Classification:

• 60E10
• 60J05
• 62E15

Acknowledgments

The author would like to thank the anonymous referee for many helpful comments which led to improvement of this article. The author would also like to express her appreciation to one of the anonymous reviewers whose work on computer graphics and simulations enhanced the readability and completeness of this article.