A general algorithm for computing simultaneous prediction intervals for the (log)-location-scale family of distributions. Issue 8 (24th May 2017)

• Record Type: Journal Article
• Authors: Xie, Yimeng; Hong, Yili; Escobar, Luis A.; Meeker, William Q.
• Is Part Of: Journal of statistical computation and simulation. Volume 87:Issue 8(2017)
• Page Start: 1559
• Page End: 1576
• Publication Date: 2017-05-24
• Subjects: Censored data -- coverage probability -- k out of m -- lognormal -- simulation -- Weibull; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2016.1277426
• Languages: English
• ISSNs: 0094-9655

Abstract

ABSTRACT: 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.