Information analysis for past life based on geometric vitality function of k-records

The past geometric vitality function is a helpful tool in reliability and survival studies for describing various properties of a system when it breaks down in (0,t). In this article, we introduce the concept of past GVF in k-records and give the expression of the proposed measure in terms of expectation of truncated gamma distributed random variable arising from any continuous distribution. In the context of information, the study describes the importance of constructing k-records from a random sample. Further, some well-known properties were analyzed using the proposed measure. The study establishes a simple estimator for the past GVF of k-records and presents a numerical illustration based on a real-life data set. In addition to this, we present the numerical comparison of performance of past GVF, cumulative past entropy and dynamic cumulative past entropy in the context of k-records with the help of a real data set. Finally, based on a real-life data set we discuss the aging pattern of the system based on past GVF of k-record values.