A general algorithm for computing simultaneous prediction intervals for the (log)-location-scale family of distributions

Abstract

<p>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 <em>k</em> out of <em>m</em> future observations with a certain confidence level based on <em>n</em> previous observations from the same distribution. A closely related problem is to obtain a one-sided upper (or lower) simultaneous prediction bound (SPB) to exceed (or be exceeded) by at least <em>k</em> out of <em>m</em> future observations. In this paper, we provide a general approach for computing SPIs and SPBs based on data from a particular member of the (log)-location-scale family of distributions with complete or right censored data. The proposed simulation-based procedure can provide exact coverage probability for complete and Type II censored data. For Type I censored data, our 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.</p>