Optimal random sample size based on Bayesian prediction of exponential lifetime and application to real data

Abstract

Choosing the sample size is a problem faced by anyone doing a survey of any type. What sample<br><br>size do we need?" is one of the most frequently asked questions of statisticians. The answer always<br><br>starts with It depends on ...". In this paper, we respond to this question by considering two criteria,<br><br>total cost of experiment and mean squared prediction error in prediction problem. Towards this end,<br><br>we discuss the problem of Bayesian predicting future observations from an exponential distribution<br><br>based on an observed sample, when the information sample size is fixed as well as a random variable.<br><br>Some distributions for the information sample size are considered and then for each case we find the<br><br>parameter of distribution of the information sample size, such that the point predictor of a future<br><br>order statistic has minimum mean squared prediction error when the total cost of experiment is<br><br>bounded. To show the usefulness of our results, we present a simulation study. Finally, we apply our<br><br>results to some real data sets in life testing.