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Abstract In statistical literature, various probability distributions exist with advantageous properties, while others are considered pathological since their properties are counterintuitive. A well-known pathological probability distribution is the Cauchy distribution, and it has applications in areas related to environmental and financial research. Both the log-Cauchy and half-Cauchy distributions, which have close connections to the Cauchy distribution, are pathological distributions. This paper considers another pathological model called the Cauchy Birnbaum-Saunders distribution. Some of the statistical properties of this distribution are discussed briefly, and its parameters are estimated using eight frequentist estimation methods, including the maximum likelihood, least-squares-based, and minimum distance estimation methods. Monte Carlo simulations are carried out to compare and examine the performance of each estimator numerically. Furthermore, a recent climate data set is analyzed to show the practical applicability of this model. Downloads PDF Published 2022-08-26 How to Cite Alam, F. M. A. (2022). On Comparing Different Methods of Estimation for the Parameters of a Pathological Distribution with Application to Climate Data. Austrian Journal of Statistics, 51(4), 120–147. https://doi.org/10.17713/ajs.v51i4.1331 More Citation Formats ACM ACS APA ABNT Chicago Harvard IEEE MLA Turabian Vancouver Download Citation Endnote/Zotero/Mendeley (RIS) BibTeX Issue Vol. 51 No. 4 (2022): Regular Issue Section Articles License Copyright (c) 2022 Farouq Mohammad A. Alam

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