A Comparison of Conditional and Unconditional Inference Relating to Log-Gamma Distribution

The family of log-gamma distributions, with varying values of the shape parameter k, provides a wide range of distributions including the extreme value and normal. In this paper, we shall discuss some inferential issues relating to this family of distributions based on censored samples. First, by assuming the shape parameter k to be known, we discuss maximum likelihood estimation of location and scale parameters. Then we describe the construction of the confidence intervals conditionally and unconditionally for these parameters. We also make a comparison of the conditional and unconditional methods of constructing confidence intervals. Finally, we illustrate these methods of inference with a numerical example.