Improved Likelihood Inference Procedures for the Logistic Distribution

Abstract

We consider third-order likelihood inferences for the parameters, quantiles and reliability function of the logistic distribution. This theory involves the conditioning and marginalization of the likelihood function. The logistic distribution is a symmetric distribution which is closely related to normal distributions, and which has several applications because of its mathematical tractability and the availability of a closed-form cumulative distribution function. The performance of the third-order techniques is investigated and compared with the first-order techniques using simulations. The results show that the third-order techniques are far more accurate than the usual first-order inference procedures. This results in more accurate inferences about the functions of the parameters of the distribution, which leads to more precise conclusions about the phenomenon modeled by the logistic distribution.

Keywords

• likelihood ratio statistic
• third order inference
• logistic distribution
• ancillary directions
• conditioning
• Barndorff-Nielsen’s formula