On Comparing Different Methods of Estimation for the Parameters of a Pathological Distribution with Application to Climate Data

Austrian Journal of Statistics

article

Farouq Mohammad A. Alam¹ 

[1] King Abdulaziz University

关键词: Cauchy Birnbaum-Saunders distribution;    Birnbaum-Saunders distribution;    maximum likelihood estimation;    least-square-based estimation;    minimum distance estimation;   

DOI  :  10.17713/ajs.v51i4.1331

学科分类：医学（综合）

来源: Austrian Statistical Society

【 摘 要 】

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.

【 授权许可】

CC BY