Asymptotic results in partially non-regular log-exponential distributions

We propose approximations to the moments, different possibilities for the limiting distributions and approximate confidence intervals for the maximum-likelihood estimator of a given parametric function when sampling from partially non-regular log-exponential models. Our results are applicable to the two-parameter exponential, power-function and Pareto distribution. Asymptotic confidence intervals for quartiles in several Pareto models have been simulated. These are compared to asymptotic intervals based on sample quartiles. Our intervals are superior since we get shorter intervals with similar coverage probability. This superiority is even assessed probabilistically. Applications to real data are included.