Distribution-free prediction intervals for order statistics based on record coverage

Abstract

a b s t r a c tIn this paper, based on the largest and smallest observations at the times when a new record of either kind (upper or lower) occurs, we discuss the prediction of future order statistics. The proposed prediction intervals are distribution-free in that the corresponding coverage probabilities are known exactly without any assumption about the parent distribution other than that it being continuous. An exact expression for the prediction coefficient of these intervals is derived. Similarly, prediction intervals for future records based on observed order statistics are also obtained. Finally, two real-life data, one involving the average July temperatures in Neurenburg, Switzerland, and the other involving the amount of annual rainfall at the Los Angeles Civic Center, are used to illustrate the procedures developed here.

On Distributional Properties of Record Ranges and Record Range Times

“…These two concepts have been studied by many authors. For instance, an application of record range was considered and some characterization results were derived by Basak [15], Ahmadi and Balakrishnan [16] obtained confidence intervals for quantiles in terms of record range, Ahmadi and Balakrishnan [17] gave distribution-free confidence intervals based on current records, Raqab [18] found inequalities for expected current record statistics, Raqab [19] and Ahmadi and Balakrishnan [20] considered distribution-free prediction intervals based on current records and record coverage.…”

Prediction Intervals for Progressive Type-II Right-Censored Order Statistics from Two Independent Sequences

“…Distribution-free two-sided prediction intervals (DFPIs) are interest of natural in this article. Many contexts have taken place in the DFPIs direction in recent years by using several assumption; see, for example [1][2][3][4][5][6][7][8][9][10][11]. Recently, DFPIs for future progressively Type-II right-censored order statistics sample (PCOs) (which it's cdf purposed by Kamps and Cramer [12]) based on k-records [13].…”

Estimation for Two-Parameter Generalized Exponential Distribution Based on Records

“…Soliman et al (2006) obtain Bayes estimators based on record statistics for two unknown parameters of the Weibull distribution. Recently, Ahmadi and Balakrishnan (2011) discuss the prediction of future order statistics based on the largest and smallest observations when there is a new record.…”