Exact Bayesian Prediction of Exponential Lifetime Based on Fixed and Random Sample Sizes

Abstract

We consider the problem of predictive intervals for future observations from an exponential distribution. We consider the following two cases: (i) fixed sample size (FSS), and (ii) random sample size (RSS). Further, we derive the predictive function for both FSS and RSS in closed forms. Next, the upper and lower 1%, 2.5%, 5% and 10% critical points for the predictive functions are calculated. To show the usefulness of our results, we present some simulation examples. Finally, we apply our results to some real data sets in life testing given in Lawless [16].

Key Words:

• Bayesian prediction
• order statistics
• predictive function
• predictive intervals
• random sample size

Additional information

Notes on contributors

A.H. Abd Ellah

Khalaf S. Sultan He is an Associate Professor in the Department of Statistics and Operations Research, King Saud University. His research interests include statistical inference, order statistics, goodness of fit tests and mixtures. He is the co-author of several book chapters in Handbook of Statistics (Eds. N. Balakrishnan and C.R. Rao) and in Stochastic Simulation Methods (Eds. N. Balakrishnan, S. Ermakov and V. Melas). His publications have appeared in the statistical literature.

K.S. Sultan

Ahmed H. Abd Ellah He is an Assistant Professor in the Department of Mathematics, Teachers College, Riyadh, Saudi Arabia. His interests are in the areas of statistical inference, distribution theory, and prediction. His publications have appeared in the statistical literature.