General cumulative Kullback–Leibler information. Issue 7 (3rd April 2018)

• Record Type: Journal Article
• Authors: Park, Sangun; Noughabi, Hadi Alizadeh; Kim, Ilmun
• Is Part Of: Communications in statistics. Volume 47:Issue 7(2018)
• Page Start: 1551
• Page End: 1560
• Publication Date: 2018-04-03
• Subjects: Cumulative entropy -- cumulative residual entropy -- empirical distribution function -- normality test.; 62F03 -- 62G10; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2017.1321767
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: 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.