Quantile based Past Geometric Vitality Function of Order Statistics

Nair and Rajesh (2000) introduced the geometric vitality function, which explains the failure pattern of components or systems based on the component's geometric mean of the remaining lifetime. Recently quantile-based studies have found greater interest among researchers as an alternative method of measuring the uncertainty of a random variable. The quantile-based measures possess some unique properties to the distribution function approach. The present paper introduces a quantile-based past geometric vitality function of order statistics and its properties. Finally, we provide an application for the new measure based on some distributions which are useful in lifetime data analysis.