Some new results involving residual Renyi's information measure for $k$-record values

This article dealt with further properties of the Renyi entropy and the residual Renyi entropy of $k$-record values. First, we discussed the Renyi entropy order and its connection with the usual stochastic and dispersive orders. We then addressed the monotonicity properties of the residual Renyi entropy of $k$-records, focusing on the aging properties of the component lifetimes. We also expressed the residual $n$th upper $k$-records in terms of Renyi entropy when the first dataset exceeded a certain threshold, and then studied various properties of the given formula. Finally, we conducted a parametric estimation of the Renyi entropy of the $n$th upper $k$-records. The estimation was performed using both real COVID-19 data and simulated data.