Tolerance Bounds for Log Gamma Regression Models

Abstract

Finding lower confidence bounds for the quantiles of Weibull populations has received much attention in recent literature. An accurate procedure (based on solving a quadratic equation) is presented in (1.17). It is, in fact, more accurate than the currently available Monte Carlo tables. It extends to any location-scale family; this article shows that it is accurate for all members of the log gamma (K) family with ½ ≤ K ≤ ∞. The procedure is shown to work well for censored data. It also extends naturally to regression data. An even more accurate procedure (an approximation to the Lawless conditional procedure, in which the “configurations” are replaced by an approximation of their expected values) is presented in (3.1). It involves numerical integration, but the tables are independent of the data. It extends easily to the censored case.

KEY WORDS:

• Tolerance bounds
• Log gamma distribution
• Censoring
• Closed form approximation
• Tables for approximate conditional approximation