Optimal Prediction and Tolerance Intervals for the Ratio of Dependent Normal Random Variables

Abstract

A simple exact method is proposed for computing prediction intervals and tolerance intervals for the distribution of the ratio X1/X2 when (X1,X2) follows a bivariate normal distribution. The methodology uses the factors available for computing one-sample prediction intervals and tolerance intervals for a univariate normal distribution. Both one-sided and two-sided intervals are constructed, and the two-sided tolerance intervals are obtained with and without imposing the equal-tail requirement. The results are illustrated using two practical applications that call for the computation of prediction intervals and tolerance intervals for the distribution of the ratio X1/X2. The
first application is an investigation of retroviral contamination in the raw materials used for the manufacture of the influenza vaccine FluMist. The second application is on the cost-effectiveness of a new drug compared to a standard drug.

IJSS, Vol. 25(1), March, 2025, pp 11-22