Title : ( On weighted cumulative residual entropy )
Authors: MALIHEH MIR ALI , Simindokht Baratpour Bajgiran , Vahid Fakoor ,
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Abstract
In analogy with the weighted Shannon entropy proposed by Belis and Guiasu (1968) and Guiasu (1986), we introduce a new information measure called weighted cumulative residual entropy (WCRE). This is based on the cumulative residual entropy (CRE), which is introduced by Rao et al. (2004). This new information measure is “length biased” shift-dependent that assigns larger weights to larger values of random variable. The properties of WCRE and a formula relating WCRE and weighted Shannon entropy are given. Related studies of reliability theory is covered. Our results include inequalities and various bounds to the WCRE. Conditional WCRE and some of its properties are discussed. The empirical WCRE is proposed to estimate this new information measure. Finally strong consistency and central limit theorem are provided.
Keywords
, Conditional entropy, Cumulative residual entropy, Empirical entropy, Maximum entropy, Mean residual life, Survival function, Weighted Shannon entropy
@article{paperid:1055788,
author = {MIR ALI, MALIHEH and Baratpour Bajgiran, Simindokht and Fakoor, Vahid},
title = {On weighted cumulative residual entropy},
journal = {Communications in Statistics - Theory and Methods},
year = {2017},
volume = {46},
number = {6},
month = {May},
issn = {0361-0926},
pages = {2857--2869},
numpages = {12},
keywords = {Conditional entropy; Cumulative residual entropy; Empirical entropy; Maximum entropy; Mean residual life; Survival function; Weighted Shannon entropy},
}
%0 Journal Article
%T On weighted cumulative residual entropy
%A MIR ALI, MALIHEH
%A Baratpour Bajgiran, Simindokht
%A Fakoor, Vahid
%J Communications in Statistics - Theory and Methods
%@ 0361-0926
%D 2017
