On Some Relations Linking Exponential and Geometrical Record Random Variables

Various record achievements are recorded in a number of areas of human activity. In this case, some discretization of the obtained observation results repeatedly occurs with varying accuracy (up to a second, up to a meter, and up to a thousand individuals). Using exponential and geometric distributions as an example, we show how such a transition from continuous to discrete probability distributions changes the number of record values in the corresponding sequences of random variables.