A Generalized Measure of Cumulative Residual Entropy |
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| Authors: | Sudheesh Kumar Kattumannil E P Sreedevi Narayanaswamy Balakrishnan |
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| Institution: | 1.Applied Statistics Unit, Indian Statistical Institute, Chennai 600029, India;2.Department of Statistics, SNGS College, Pattambi 679306, India;3.Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada; |
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| Abstract: | In this work, we introduce a generalized measure of cumulative residual entropy and study its properties. We show that several existing measures of entropy, such as cumulative residual entropy, weighted cumulative residual entropy and cumulative residual Tsallis entropy, are all special cases of this generalized cumulative residual entropy. We also propose a measure of generalized cumulative entropy, which includes cumulative entropy, weighted cumulative entropy and cumulative Tsallis entropy as special cases. We discuss a generating function approach, using which we derive different entropy measures. We provide residual and cumulative versions of Sharma–Taneja–Mittal entropy and obtain them as special cases this generalized measure of entropy. Finally, using the newly introduced entropy measures, we establish some relationships between entropy and extropy measures. |
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| Keywords: | cumulative entropy cumulative residual entropy extropy Tsallis entropy weighted cumulative residual entropy |
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