Abstract
The log-logistic distribution is a useful distribution in survival analysis. Parameter estimation problems have been discussed by many authors. This paper focuses on the interval estimation for the shape parameter of the log-logistic distribution. Bain and Engelhardt3 gave confidence intervals for the parameters of a logistic distribution based on pivotal quantities formed by maximum likelihood estimators. Chen10 proposed another method for obtaining exact confidence intervals of the shape parameter of the log-logistic distribution. Compared with the existing methods for constructing confidence intervals for the parameters of the log-logistic distribution, the method given in Chen10 is easier to use. In the present paper, the pivotal quantity used in Chen10 is adjusted to improve the performance of statistical analysis. Monte Carlo simulation is conducted to compare the performance of different pivotal quantities. The simulation result shows that the adjusted pivotal quantity has better performance, and then should be recommended to the statistics users.
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