On cumulative residual information generating function: properties, inference and applications

We consider a new information generating function introduced by Kharazmi and Balakrishnan (Commun Stat Theory Methods 52(15):5260–5273, 2023), called cumulative residual information generating (CRIG) function and study some new properties. Also we find that the CRIG function has a relationship with many popular measures like Gini’s mean difference, cumulative residual Tsallis entropy and cumulative residual extropy. We obtain numerous bounds for CRIG function and study characterization in terms of CRIG of first order statistic. We propose two non-parametric estimators of CRIG function and investigate their asymptotic properties. Based on one of the proposed estimators, a new test statistic for testing equality of two distribution functions is developed. Finally, CRIG function for mixed systems is analyzed and complexity of systems is studied.