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

Xie, Yimeng
Hong, Yili
Meeker, William
Escobar, Luis
Meeker, William
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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 one-sided 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 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>This is an Accepted Manuscript of an article published by Taylor & Francis as Xie, Yimeng, Yili Hong, Luis A. Escobar, and William Q. Meeker. "A general algorithm for computing simultaneous prediction intervals for the (log)-location-scale family of distributions." <em>Journal of Statistical Computation and Simulation</em> 87, no. 8 (2017): 1559-1576. DOI: <a href="http://dx.doi.org/10.1080/00949655.2016.1277426" target="_blank">10.1080/00949655.2016.1277426</a>. Posted with permission.</p>
Censored data, coverage probability, k out of m, lognormal, simulation, Weibull