On some relationships between records in the transition from continuous to discrete distributions

Abstract

In the present work, we consider discretization of continuous distributions and study relations between continuous record values, weak record values and discrete record values obtained from continuous record values by discretization. We first compare the numbers of continuous record values registered in real intervals and the numbers of discrete record values and weak record values located on the sets of non-negative integers. Further in the paper, we introduce the so-called strong continuous record values that hold out after discretization and we discuss their distributional properties. We also analyze what happens with record values after discretization of the standard exponential distribution. Finally, we present a simulation experiment, which supports the theoretical results of the paper.