Publication Date


Series Number

Preprint #2014-06


Making predictions of future realized values of random variables based on currently available data is a frequent task in statistical applications. In some applications, the interest is to obtain a two-sided simultaneous prediction interval (SPI) to contain at least k out of m future observations with a certain confidence level based on n previous observations from the same distribution. A closely related problem is to obtain a onesided upper (or lower) simultaneous prediction bound (SPB) to exceed (or be exceeded) by at least k out of m future observations. In this paper, we provide a general approach for constructing SPIs and SPBs based on data from a member of the (log)-location-scale family of distributions with complete or right censored data. The proposed simulationbased procedure can provide exact coverage probability for complete and Type II censored data. For Type I censored data, the simulation results show that our procedure provides satisfactory results in small samples. We use three applications to illustrate the proposed simultaneous prediction intervals and bounds.


This preprint was published as Yimeng Xie, Yili Hong, Luis A. Escobar, and William Q. Meeker, "Simultaneous Prediction Intervals for the (Log)-Location-Scale Family of Distributions".