Quantile-Based Generalized Entropy of Order (α, β) for Order Statistics

Abstract

In the present paper, we propose a quantile version of generalized entropy measure for order statistics for residual and past lifetimes and study their properties. Lower and upper bound of the proposed measures are derived. It is shown that the quantile-based generalized information between i-th order statistics and parent random variable is distribution free. The uniform, exponential, generalized Pareto and finite range distributions, which are commonly used in the reliability modeling have been characterized in terms of the proposed entropy measure with extreme order statistics.

Keywords

• Quantile function
• Quantile entropy
• Reliability measures
• Series and parallel system