Prediction of future generalized order statistics based on two-parameter exponential distribution for large samples

ABSTRACT

Exact and asymptotic distributional properties are discussed in detail for two mean-squared error consistent point predictors of future-generalized order statistics (GOSs) based on two-parameter exponential distribution. These predictors work even if some observed data were missing. For each point predictor, the asymptotic distribution of the normalized difference between the future GOS and its point predictor is derived, when the scale parameter is known or unknown. It is revealed that the asymptotic distributions of these normalized differences are equal when the scale parameter is known. Two asymptotic prediction intervals of the future GOS are constructed whenever the scale parameter is known or unknown. Furthermore, two tests of outliers are proposed relying on the point predictors. Finally, a simulation study is conducted and a real data set is analyzed for illustrative purposes.

KEYWORDS:

• Generalized order statistics
• mean-squared-error consistency
• monte carlo simulation
• point prediction
• probability coverage
• weak convergence

Acknowledgments

This work was funded through the Plan ‘Science UP Faculty of Science’ from the National Academy of Scientific Research and Technology of Egypt, project number 6714. The authors are grateful to the editorial board and the referees for suggestions that improved the presentation substantially.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Funding This work was funded through the Plan “Science UP Faculty of Science” from the National Academy of Scientific Research and Technology of Egypt, project number 6656.

Notes on contributors

H. M Barakat

H. M. Barakat is a Professor of Mathematical Statistics at Zagazig University. He received a Ph.D. degree in 1986 in mathematical statistics from Moscow State University. His research interests are in the areas of statistical ordered data and its applications. He has published research articles in reputed international journals of mathematical statistics. He is a referee and editor of mathematical journals. In 1999, he was awarded the Egyptian State Prize in mathematics. In 2007, he was awarded the State Award for Excellence in Basic Science. In 2010, he was awarded the Discretionary Zagazig University Prize, and in 2012, he was awarded the International Fiza Al-Kharafi Prize in the field of Mathematics.

Magdy E El-Adll

Magdy E. El-Adll is a Professor of Mathematical Statistics at Helwan University. He received his Ph.D. degree in 2003 in Mathematical Statistics from Zagazig University. His research interests focus on ordered random variables and their applications. He has published research articles in reputed international journals of statistics. He is a referee in some international statistical journals.

Amany E Aly

Amany E. Aly is an Associate Professor at Helwan University. She received her Ph.D. degree in 2003 from the Department of Mathematics at Helwan University. She has published research articles in reputed international statistical journals. Her research interests are in the areas of ordered statistical data and its applications.