In this paper, the quantile function is recalled and some reliability measures are rewritten in terms of quantile function. Next, quantile based dynamic cumulative residual entropy is obtained and some of its properties are presented. Then, some characterization results of uniform, exponential and Pareto distributions based on quantile based dynamic cumulative entropy are provided. A simple estimator is also proposed and its performance is studied for exponential distribution. Finally discussion and results are presented.

This paper first introduces the Kerridge inaccuracy measure as an extension of the Shannon entropy and then the measure of past inaccuracy has been rewritten based on the concept of quantile function. Then, some characterizations results for lifetimes with proportional reversed hazard model property based on quantile past inaccuracy measure are obtained. Also, the class of lifetimes with increasing (decreasing) quantile past inaccuracy property and some of its properties are studied. In addition, via an example of real data, the application of quantile inaccuracy measure is illustrated.

Entropy plays a fundamental role in reliability and system lifetesting areas. In the recent studies, much attentions have been paid to use quantile functions properties and their applications as an alternate approac in distinguishing statistical models and analysis of data. In the present paper, quantile based residual Tsallis entropy is introduced and its properties in continuous models are investigated. Considering distributions of certain lifetime, explicit versions for quantile based residual Tsallis entropy are obtained and their properties monotonicity are studied and characterization based on this entropy is investigated. Also quantile based Tsallis divergence is introduced and quantile based residual Tsallis divergence is obtained. Finally, an estimator for the quantile based residual Tsallis entropy is introduced and its performance is investigate by study simulation.