Distribution theory of δ-record values: case δ≥0
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Fernando López-Blázquez [1] ; Begoña Salamanca-Miño [1]
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[1] Universidad de Sevilla
Universidad de Sevilla
Sevilla, España
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- Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 24, Nº. 3, 2015, págs. 558-582
- Idioma: inglés
- DOI: 10.1007/s11749-014-0424-0
- Texto completo no disponible (Saber más ...)
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Resumen
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.
