# Bayesian approach to prediction and the spacings in the exponential distribution

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## Summary

A series of independent samples are drawn from a general population with positive variation*f(x,ϕ), x>0*. Based on the Bayesian approach, a general predictive distribution is given, to predict a statistic in the future sample based on the statistics in the earlier samples (or stages). Few general classes of distributions of this type like Koopman-Pitman family, power function family and Burr's class of distributions are considered to show how this procedure works in predicting order statistics in the future sample. Also, the sum of the spacings in the future samples from an exponential population is predicted in terms of similar sum of spacings in the earlier samples. Discussion on the variance of this predictive distribution is dealt with. Finally, an illustrative example with simulated samples from an exponential population gives actual prediction of an order statistic as well as the sum of spacings in the future sample.

### Keywords

Order Statistic BAYESIAN Approach Prediction Interval Predictive Distribution Life Testing## Preview

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