The future occurrence of records

Abstract

SummaryThe occurrence of future record values based on data from a sequence of independent, identically distributed random variables is considered. Two situations are analysed, namely (i) where only the first m record observations have been noted, and (ii) where all the observations have been noted up to the ruth record. Tolerance regions and Bayesian predictive distributions are derived for the increase in size of the (m-}-r)th record value over the observed ruth record value for two exponential models. Predictive distributions are also given for the additional number of observations required after the ruth record value until the (m+l)th record value occurs.

Shrinkage Testimation in Exponential Distribution based on Records under Asymmetric Squared Log Error Loss

“…Consider a data set discussed by Dunsmore (1983). A rock crushing machine is kept working as long as the size of the crushed rock is larger than the rocks crushed before.…”

On Performance of Reconstructed Middle Order Statistics in Exponential Distribution

“…Consider a data set concerning the rock crushing machine which was reported by Dunsmore (1983) as a real data set where comes from the exponential distribution. A rock crushing machine has to be reset if at any operation the size of the rock being crushed is larger than the rock that has been crushed before.…”

Prediction intervals for future records and order statistics coming from two parameter exponential distribution

“…Several authors have studied the subject of predicting future records on the basis of observed records from the same distribution. See for example, Ahsanullah (1980), Dunsmore (1983), Awad and Raqab, Mohammad (2000), Ali Mousa et al (2002), Ahmadi et al (2005), Ahmadi and Doostparast (2006), Raqab (in press), Raqab and Balakrishnan (2008), Ahmadi et al (in press) and the references therein. Thus, so far, researchers have considered prediction of records based on records and prediction of order statistics based on order statistics.…”