Quantile based Tsallis entropy in residual lifetime

A.H. Khammar and S.M.A. Jahanshahi

Physica A: Statistical Mechanics and its Applications, 2018, vol. 492, issue C, 994-1006

Abstract: Tsallis entropy is a generalization of type α of the Shannon entropy, that is a nonadditive entropy unlike the Shannon entropy. Shannon entropy may be negative for some distributions, but Tsallis entropy can always be made nonnegative by choosing appropriate value of α. In this paper, we derive the quantile form of this nonadditive’s entropy function in the residual lifetime, namely the residual quantile Tsallis entropy (RQTE) and get the bounds for it, depending on the Renyi’s residual quantile entropy. Also, we obtain relationship between RQTE and concept of proportional hazards model in the quantile setup. Based on the new measure, we propose a stochastic order and aging classes, and study its properties. Finally, we prove characterizations theorems for some well known lifetime distributions. It is shown that RQTE uniquely determines the parent distribution unlike the residual Tsallis entropy.

Keywords: Residual quantile Tsallis entropy; Quantile function; Proportional hazards model; Reliability measures; Stochastic comparisons; Characterizations (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:492:y:2018:i:c:p:994-1006

DOI: 10.1016/j.physa.2017.11.030

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