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Vlastnosti Cauchyho rozdělení a jejich užití: Properties of Cauchy Distribution and their Applications

by Samson Quaye

Institution:	Brno University of Technology
Department:
Degree:
Year:	2022
Keywords:	Cauchyho rozdělení; odhad parametrů; Huberův M-estimátor; Hodges Lehmannův odhad; Trimmed Mean; Sens Mean; ROC křivky.; Cauchy distribution; Parameter estimation; Huber M-estimator; Hodges Lehmann estimator; Trimmed Mean; Sens Mean; ROC curves.
Posted:	3/25/2025
Record ID:	2292392
Full text PDF:	http://hdl.handle.net/11012/208447

Abstract

The Cauchy distribution plays a major role in biology, mathematics, physics and many related disciplines. As a consequence, a parameter estimation methodology for data which is distributed according to a Cauchy distribution is of importance. Nevertheless, the Cauchy distribution is well known for causing difficulties with classical approaches to parameter estimation. This diploma thesis is concerned with the study of the properties of Cauchy distribution. Several robust estimators of its location parameter are presented. A simulation study programmed in Python allows us to compare the performance of these parameter estimates in Bi-Cauchy ROC curve estimation. Moreover, some theoretical properties of the Bi-Cauchy ROC curve are studied.