Prediction intervals of future observations for a sample of random size from any continuous distribution

Abstract

In this paper, a general method for predicting future observations from any arbitrary continuous distribution is proposed. Two pivotal statistics are developed to construct prediction intervals of future observations in two cases. In the first case, we assume fixed sample size, while in the second case, the sample size is assumed to be positive integer-valued random variable independent of the observations. Explicit forms for the distribution functions of the pivotal statistics are derived. Some special cases for the random sample size are considered. An algorithm is constructed to demonstrate the practical importance of the theoretical results. Moreover, simulation study is applied on some important distributions to investigate the efficiency of the suggested method. Finally, an example for real lifetime data is analyzed, where it is assumed that the distribution of the data is unknown.