Approximate Inference for the Generalized Gamma Distribution

Abstract

Methods of approximate conditional inference in location and scale parameter distributions, based on normal approximations to the distributions of signed square roots of likelihood ratio statistics, are discussed. These methods are applied to obtain approximate inference for the quantiles and scale parameter of the log generalized gamma distribution from uncensored samples, assuming that the index parameter of the distribution is known. As special cases, approximate inference in the extreme value and normal distributions from Type II censored samples is considered. The accuracy of the approximate methods for small samples is illustrated by comparison with exact results in some examples.

KEY WORDS:

• Approximate conditional inference
• Asymptotics
• Censoring
• Likelihood ratio statistics
• Location-scale models
• Tolerance bounds