Some extensions of entropy and KL information to the survival function have been recently proposed. We first compare some extensions of KL information and provide a criterion in choosing one among those extensions. Then we study moment constraints for maximum cumulative residual entropy distribution(Rao etal., 2004) in view of the relation between the cumulative residual entropy difference and cumulative residual Kullback-Leibler (KL) information. We further discuss the estimation methods and suggest a weighted cumulative residual entropy. Finally, we discuss the application of the estimated cumulative residual KL information as a goodness of fit test statistic with numerical examples.
Bibliographical noteFunding Information:
The authors are grateful to two anonymous referees and an associate editor for making some useful comments on an earlier version of this manuscript. Park’s work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (Nos 2011-0029104 and 2012-004905 ).
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty