Quantile-Based Shannon Entropy for Record Statistics

The quantile-based entropy measures possess some unique properties than their distribution function approach. The present communication deals with the study of the quantile-based Shannon entropy for record statistics. In this regard a generalized model is considered for which cumulative distribution function or probability density function does not exist and various examples are provided for illustration purpose. Further we consider the dynamic versions of the proposed entropy measure for record statistics and also give a characterization result for that. At the end, we study Fα\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F^{\alpha }$$\end{document}-family of distributions for the proposed entropy measure.