Information generating function based on records for residual lifetime variables

In this paper, we employ the residual information generating function to quantify the information content in the remaining lifetime of a component or system based on record values. Moreover, analytical expressions of this function are derived for record values obtained from sequences of random variables under location-scale and monotone transformations. Two new classes of distributions and a corresponding stochastic order are introduced based on the proposed measure. It is further established that the hazard rate function of records uniquely determines their residual information generating function. Key properties of the residual information generating function of records such as monotonicity, stochastic ordering, and theoretical bounds are analyzed. Moreover, a characterization of the parent distribution through the residual information generating function of records is provided. Finally, the study introduces straightforward estimators for the residual information generating function, applicable to both record values and the underlying parent distribution. Furthermore, numerical illustrations were conducted using two real life data sets to evaluate the performance of the proposed estimators.