Multivariate quantile inactivity time with medical applications

The concept of α-quantile inactivity time was developed for situations with bivariate or multivariate random lifetimes. In this situation, each element has a specific history related to itself, indicating that the corresponding event occurred earlier. The behavior of the α-quantile inactivity time was specifically studied in relation to the corresponding multivariate hazard rate function. Applying the empirical bivariate distribution function, an estimator for the bivariate α-quantile inactivity time function is introduced. The asymptotic properties of the empirical distribution function and Taylor expansion are used to discuss its asymptotic behavior. Subsequently, the behavior of the proposed estimator was investigated in a simulation study. Finally, the applicability of the proposed concept and its estimator is illustrated by analyzing a dataset in the context of medical sciences.