Current records and record range with some applications

• Published in: Journal of the Korean Statistical Society Vol. 43; no. 2; pp. 263 - 273
• Main Authors: Barakat, H.M., Nigm, E.M., Aldallal, R.A.
• Format: Journal Article
• Language: English
• Published: Singapore Elsevier B.V 01.06.2014; Springer Singapore; 한국통계학회
• Subjects: Applied Statistics; Bayesian Inference; Current records; Negative Pareto distribution; Pareto distribution; Positive Weibull distribution; Record range; Recurrence relations; Statistical Theory and Methods; Statistics; Statistics and Computing/Statistics Programs; Stopping time; Weak convergence; Weibull distribution; 통계학; secondary; Weak convergence; Stopping time; Pareto distribution; Record range; Positive Weibull distribution; Weibull distribution; Current records; Recurrence relations; Negative Pareto distribution; primary; primary 62G30; secondary 62G15
• ISSN: 1226-3192; 2005-2863
• DOI: 10.1016/j.jkss.2013.09.004

In a sequence of independent and identically distributed (iid) random variables, the upper (lower) current records and record range are studied. We derive general recurrence relations between the single and product moments for the upper and lower current records based on Weibull and positive Weibull distributions, as well as Pareto and negative Pareto distributions, respectively. Moreover, some asymptotic results for general current records are established. In addition, a recurrence relation and an explicit formula for the moments of record range based on the exponential distribution are given. Finally, numerical examples are presented to illustrate and corroborate theoretical results.