Abstract
In this paper, we use the r smallest Type-II censored order statistics X 1:n ≤ X 2:n ≤ ... ≤ X r:n from the uniform distribution to predict the upper bound for the remaining n − r observations. We use a certain statistic based both classical and Bayesian approaches. In order to show the efficiency of the proposed techniques, we point out some numerical illustrations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abd Ellah, A.H., Sultan, K.S.: Exact Bayesian Prediction of Exponential Lifetime Based on Fixed and Random Sample Sizes. Quality Technology & Quantitative Management 2, 161–175 (2005)
Adatia, A., Chan, L.K.: Robust Procedures for Estimating the Scale Parameter and Predicting Future Order Statistics of the Weibull Distribution. IEEE Trans. Reliability R-31(5), 491–498 (1982)
Arnold, B.C., Balakrishnan, N., Nagaraja, H.N.: A First Course in Order Statistics. John Wiley & Sons, New York (1992)
Balasooriya, U.: A Comparison of the Prediction of Future Order Statistics for the 2-Parameter Gamma Distribution. IEEE Trans. Reliability R-36(5), 591–594 (1987)
Lawless, J.F.: A prediction problem concerning samples from the exponential distribution, with application in life testing. Technometrics 13, 725–730 (1971)
Lingappaiah, G.: Prediction in exponential life testing. Canad. J. Statist. 1, 113–117 (1973)
Lu, H.L.: Prediction Intervals of an Ordered Observation from One-Parameter Exponential Distribution Based on Multiple Type II Censored Samples. J. Chinese Institute of Industrial Engineers 21(5), 494–503 (2004)
Morris, K.W., Szynal, D.: A Goodness-of-Fit Test for the Uniform Distribution Based on a Characterization. J. Math. Sci. 106, 2719–2724 (2001)
Nelson, W., Schmee, J.: Prediction Limits for the Last Failure Time of a (Log) Normal Sample from Early Failures. IEEE Trans. Reliability R-30(5), 461–465 (1981)
Ogunyemi, O.T., Nelson, P.I.: Prediction of Gamma failure times. IEEE Trans. Reliability R-46(3), 400–405 (1997)
Proschan, F.: Theoretical explanation of observed decreasing failure rate. Technometrics 5, 375–383 (1963)
Samuel-Cahn, E.: Two Kinds of Repeated Significance Tests, and Their Application for the Uniform Distribution. Comm. Statist. Simulation Comput. 3(5), 419–431 (1974)
Sultan, K.S., Abd Ellah, A.H.: Exact prediction intervals for exponential lifetime based on random sample size. Int. J. Comput. Math. 83(12), 867–878 (2006)
Steele, M., Chaseling, J.: Powers of Discrete Goodness-of-Fit Test Statistics for a Uniform Null Against a Selection of Alternative Distributions. Comm. Statist. Simulation Comput. 35, 1067–1075 (2006)
Wright, W.P., Singh, N.: A Prediction Interval in Life Testing: Weibull Distribution. IEEE Trans. Reliability R-30(5), 466–467 (1981)
Wu, T.H., Lu, H.L.: Prediction intervals for an ordered observation from the logistic distribution based on censored samples. J. Stat. Comput. Simul. 77(5), 389–405 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sultan, K.S., Alshami, S.A. (2010). Prediction of Future Order Statistics from the Uniform Distribution. In: Borgelt, C., et al. Combining Soft Computing and Statistical Methods in Data Analysis. Advances in Intelligent and Soft Computing, vol 77. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14746-3_73
Download citation
DOI: https://doi.org/10.1007/978-3-642-14746-3_73
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14745-6
Online ISBN: 978-3-642-14746-3
eBook Packages: EngineeringEngineering (R0)