Simultaneous Tolerance Intervals and Prediction Intervals for Some Multivariate Normal Populations

• Activity Number: 550
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Malick Mbodj*
• Companies: FDA
• Keywords: simultaneous tolerance intervals for some multivariate normal populations ; prediction intervals for some multivariate normal populations

Abstract

A tolerance region for a population is a region computed using a random sample, so that the region will include a specified proportion or more of the population, with a given confidence level. The theory of statistical tolerance regions has undergone vigorous development during the last several years, and approximations have been developed for computing the required tolerance factor. However, the available literature in the case of multivariate normal populations deals with the derivation of ellipsoidal tolerance regions only. The present research is motivated by the fact that an ellipsoidal tolerance region cannot provide information on the distribution of the individual components of the response vector. In the talk, I will describe accurate methodology for computing simultaneous tolerance intervals and simultaneous prediction intervals for multivariate normal distributions. The case of a general covariance matrix will be considered, and the derivation of both one-sided and two-sided simultaneous intervals will be addressed. Numerical results will be given to assess the accuracy of the proposed solutions, and illustrative examples will be provided.