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).
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All Science Journal Classification (ASJC) codes
- Statistics and Probability