An alternative to the Cauchy distribution [PDF]
MethodsX, 2019 A few generalizations of the Cauchy distribution appear in the literature. In this paper, a new generalization of the Cauchy distribution is proposed, namely, the exponentiated-exponential Cauchy distribution (EECD).
Ayman Alzaatreh
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The Cauchy Distribution in Information Theory [PDF]
Entropy, 2023 The Gaussian law reigns supreme in the information theory of analog random variables. This paper showcases a number of information theoretic results which find elegant counterparts for Cauchy distributions.
Sergio Verdú
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The Beta-Half-Cauchy Distribution [PDF]
Journal of Probability and Statistics, 2011 On the basis of the half-Cauchy distribution, we propose the called beta-half-Cauchy distribution for modeling lifetime data. Various explicit expressions for its moments, generating and quantile functions, mean deviations, and density function of the ...
Gauss M. Cordeiro, Artur J. Lemonte
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Index distribution of Cauchy random matrices [PDF]
Journal of Physics A: Mathematical and Theoretical, 2014 Using a Coulomb gas technique, we compute analytically the probability $\mathcal{P}_ ^{(C)}(N_+,N)$ that a large $N\times N$ Cauchy random matrix has $N_+$ positive eigenvalues, where $N_+$ is called the index of the ensemble. We show that this probability scales for large $N$ as $\mathcal{P}_ ^{(C)}(N_+,N)\approx \exp\left[- N^2 _C(N_+/N)\right]$,
Ricardo Marino +3 more
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Multi-Scale Image Defogging Network Based on Cauchy Inverse Cumulative Function Hybrid Distribution Deformation Convolution [PDF]
SensorsThe aim of this study was to address the issue of significant performance degradation in existing defogging algorithms under extreme fog conditions. Traditional Taylor series-based deformable convolutions are limited by local approximation errors, while ...
Lu Ji, Chao Chen
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Optimum Multilevel Thresholding for Medical Brain Images Based on Tsallis Entropy, Incorporating Bayesian Estimation and the Cauchy Distribution [PDF]
Applied SciencesEntropy-based thresholding is a widely used technique for medical image segmentation. Its principle is to determine the optimal threshold by maximizing or minimizing the image’s entropy, dividing the image into different regions or categories.
Xianwen Wang +4 more
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Statistical Inference of Truncated Cauchy Power-Inverted Topp–Leone Distribution under Hybrid Censored Scheme with Applications [PDF]
Axioms, 2023 In this article, a new two-parameter model called the truncated Cauchy power-inverted Topp–Leone (TCP-ITL) is constructed by merging the truncated Cauchy power -G (TCP-G) family with the inverted Topp–Leone (ITL) distribution.
Rania A. H. Mohamed +4 more
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An intermediate distribution between Gaussian and Cauchy distributions [PDF]
Physica A: Statistical Mechanics and its Applications, 2012 16 pages, 7 ...
Tong Liu +3 more
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Cauchy or not Cauchy? New goodness-of-fit tests for the Cauchy distribution [PDF]
Statistical Papers, 2021 AbstractWe introduce a new characterization of the Cauchy distribution and propose a class of goodness-of-fit tests for the Cauchy family. The limit distribution is derived in a Hilbert space framework under the null hypothesis. The new tests are consistent against a large class of alternatives. A comparative Monte Carlo simulation study shows that the
Bruno Ebner, Lena Eid, Bernhard Klar
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Cauchy-Distributed Functions and a Characterization of the Cauchy Distribution [PDF]
The Annals of Mathematical Statistics, 1969 A simple representation of a class of functions of Cauchy variates whose members are also Cauchy variates is given. This leads to a characterization of the Cauchy distribution.
E. J. Williams
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