Rényi information measure for a used item

Recently, in the literature, a measure of tail heaviness has been proposed based on Rényi entropy. This measure is very useful in the sense that it can be used to measure tail heaviness even for the distributions for which the kurtosis measure β2=μ4/μ22 does not exist. Nadarajah and Zografos [Nadarajah, Zografos, Information Sciences 153 (2003), 119–138] have derived the expression for this measure for different univariate continuous distributions. But, this measure can only be used for the lifetime of a new item. In case of used item, this measure needs some modification. In this paper, we have modified the measure accordingly so that it can be used in the case of used item and also for the new item. We have also derived expressions for this measure for sixteen different univariate distributions and ten other standard distributions derived from the general distributions used in reliability and survival analysis. The most of the results obtained in the literature in this direction can be obtained as particular cases of our general results.