The present paper considers a shift-dependent measure of uncertainty and its dynamic (residual) version. Various properties have been discussed. Two classes of lifetime distributions are proposed. Further, when m independent and identically distributed observations are available, an estimator of the measure under study is presented using empirical approach. In addition, large sample properties of the estimator are studied. Finally, an application of the proposed measure to the problem related to right-tail risk measure is presented.
WGCRE Increasing convex order Decreasing failure rate Combination mean residual waiting time Proportional hazard models Empirical WGCRE Risk measure
Mathematics Subject Classification (2010)
94A17 62N05 60E15
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The author would like to thank the Editor, Associate Editor and the two referees for careful reading and for their comments which greatly improved the article.
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