We consider an extension of the mean inactivity time based on a non-negative weight function. show various properties new notion, and relate it to functions interest in reliability theory information measures, such as dynamic cumulative entropy, past varentropy, weighted entropy. Moreover, comparison times, we introduce study stochastic order compare with other suitable orders. also discuss som...

Abstract We study the concept of continuous mean distance a weighted graph. For connected unweighted graphs, can be defined as arithmetic distances between all pairs vertices. This parameter provides natural measure compactness graph, and has been intensively studied, together with several variants, including its version for graphs. The analog (discrete) is points on edges Despite being very ge...