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

Date
2017-01-01
Authors
Xie, Yimeng
Hong, Yili
Meeker, William
Escobar, Luis
Meeker, William
Journal Title
Journal ISSN
Volume Title
Publisher
Source URI
Altmetrics
Authors
Research Projects
Organizational Units
Statistics
Organizational Unit
Journal Issue
Series
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.

Description
<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>
Keywords
Censored data, coverage probability, k out of m, lognormal, simulation, Weibull
Citation
Collections