Kullback-Leibler divergence: A quantile approach

Divergence measures play an important role in measuring the distance between two probability distribution functions. Kullback-Leibler divergence function is a popular measure in this class. The present paper introduces a quantile based definition of the Kullback-Leibler divergence and study its properties in the context of lifetime data analysis. We also propose the quantile versions of Kullback-Leibler divergence for residual and past lifetime random variables.