The cumulative residual Kullback–Leibler information is defined on the semi-infinite (non negative) interval. In this paper, we extend the cumulative residual Kullback–Leibler information to the whole real line and propose a general cumulative Kullback–Leibler information. We study its application to a test for normality in comparison with some competing test statistics based on the empirical distribution function including the well-known tests applied in practice like Kolmogorov–Smirnov, Cramer–von Mises, Anderson–Darling, and other existing tests.
Bibliographical noteFunding Information:
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) grant funded by the Korea government (MOE) (No. 2015R1D1A1A01056578).
All Science Journal Classification (ASJC) codes
- Statistics and Probability