On a new NBUE property in multivariate sense: an application

Abstract

Multivariate lifetime data frequently arise so it is important to consider different multivariate distributions that could be used to model aging concepts. The generalization of univariate versions has two main problems. One of them is the concept of the multivariate quantile and the other one is that the survival function valued at a multivariate quantile depends on the underlying distributions. For this reason, a new multivariate aging concept based on the upper corrected orthant is developed. This new multivariate aging is a generalization of the New Better than Used in Expectation univariate version and a characterization by using the multivariate excess wealth function is provided. Finally, data from the Comprehensive Cohort Study performed by the German Breast Cancer Study Group are analysed in order to estimate the parameters in a non-deterministic model which describes the tumor growth and to realize how this new multivariate ageing notion influences in the final results.