Exact confidence interval for the shape parameter of a log-logistic distribution

Abstract

The log-logistic distribution is a useful distribution in survival analysis. Exact confidence interval and exact statistical test about the shape parameter of a log-logistic distribution are discussed in this article. The necessary table for calculating the limits of a confidence interval or the critical values of a statistical test is obtained by Monte Carlo simulation. The method provided in this paper can be used for type II censored data. A similar result can be developed for the logistic distribution.

Keywords:

• Log-logistic distribution
• shape parameter
• exact confidence interval
• testing hypotheses
• Monte Carlo simulation