Prediction of sth Ordered Observation for the Two-Parameter Exponential Distribution

This paper deals with obtaining a prediction interval on a future observation X, in an ordered sample of size n from a two-parameter exponential distribution for the situation where some or all the first r observations X 1 < X 2 < … < X r , 1 ≤ r < s ≤ n, have been observed. The intervals are based on the statistic Z = (X s , – X r )/S v , where S v , is a function of the observations X 0 ≡ A < X 1 < X 2 < … < X r , such that X s – X r , and S v , are independent variables and 2vSv /σ has the distribution χ2(2v). The expressions for the quantiles zp are given and some problems of numerical determination of zp 's are discussed. The results can be also applied to related distributions.