Resumen de Distribution theory of δ-record values: case δ≥0

Fernando López Blázquez , Begoña Salamanca Miño

• A δ-record of a sequence of random variables is an observation that exceeds the current record by δ units. This concept is relatively recent, so there are still many unknown aspects that require further research. In this work, for δ≥0, we investigate the distribution theory of δ-record values from an iid sample from an absolutely continuous parent. We obtain recurrent expressions for the density function of δ-records and the probability mass function of inter-δ-record times. In the particular case of the exponential distribution, we show that the sequence of δ-records are distributed as the points of a (delayed) renewal process. Finally, we point out some applications of δ-records to paralyzable counters, blocks in automobile traffic, and queuing theory.