Maximum likelihood estimation for left-truncated log-logistic distributions with a given truncation point
Abstract
The maximum likelihood estimation of the left-truncated log-logistic distribution with a given truncation point is analyzed in detail from both mathematical and numerical perspectives. These maximum likelihood equations often do not possess a solution, even for small truncations. A simple criterion is provided for the existence of a regular maximum likelihood solution. In this case a profile likelihood function can be constructed and the optimisation problem is reduced to one dimension. When the maximum likelihood equations do not admit a solution for certain data samples, it is shown that the Pareto distribution is the -limit of the degenerated left-truncated log-logistic distribution. Using this mathematical information, a highly efficient Monte Carlo simulation is performed to obtain critical values for some goodness-of-fit tests. The confidence tables and an interpolation formula are provided and several applications to real world data are presented.
Cite
@article{arxiv.2210.15155,
title = {Maximum likelihood estimation for left-truncated log-logistic distributions with a given truncation point},
author = {Markus Kreer and Ayse Kizilersu and Jake Guscott and Lukas Christopher Schmitz and Anthony W. Thomas},
journal= {arXiv preprint arXiv:2210.15155},
year = {2022}
}
Comments
27 pages, 4 figures