Weighted cumulative residual Kullback–Leibler divergence: properties and applications

Weighted cumulative residual Kullback–Leibler information measure and its dynamic version are proposed and their properties are investigated. Also weighted cumulative Kullback–Leibler information measure along with its dynamic version is introduced. Monotonicity properties of the dynamic information measures are studied. A goodness-of-fit test is developed for exponential distribution using weighted cumulative residual Kullback–Leibler information measure based on complete and censored data. It is observed that proposed tests perform well for monotone decreasing hazard alternatives under censored data. Four data sets are analyzed for illustration.