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Keywords = wrapped Cauchy distribution

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20 pages, 673 KiB  
Article
Cylindrical Models Motivated through Extended Sine-Skewed Circular Distributions
by Yoichi Miyata, Takayuki Shiohama and Toshihiro Abe
Symmetry 2024, 16(3), 295; https://doi.org/10.3390/sym16030295 - 3 Mar 2024
Viewed by 1257
Abstract
A class of cylindrical distributions, which include the Weibull-von Mises distribution as a special case, is considered. This distribution is obtained by combining the extended sine-skewed wrapped Cauchy distribution (marginal circular part) with the Weibull distribution (conditional linear part). This family of proposed [...] Read more.
A class of cylindrical distributions, which include the Weibull-von Mises distribution as a special case, is considered. This distribution is obtained by combining the extended sine-skewed wrapped Cauchy distribution (marginal circular part) with the Weibull distribution (conditional linear part). This family of proposed distributions is shown to have simple normalizing constants, easy random number generation methods, explicit moment expressions, and identifiability in parameters. In particular, the marginal distribution of the circular random variable, and its conditional distribution given a linear random variable give relatively stronger skewness than those of existing cylindrical models. Some Monte Carlo simulations and real data analysis are performed to investigate the feasibility and tractability of the proposed models. Full article
(This article belongs to the Special Issue Research Topics Related to Skew-Symmetric Distributions)
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28 pages, 850 KiB  
Article
An Universal, Simple, Circular Statistics-Based Estimator of α for Symmetric Stable Family
by Ashis SenGupta and Moumita Roy
J. Risk Financial Manag. 2019, 12(4), 171; https://doi.org/10.3390/jrfm12040171 - 23 Nov 2019
Cited by 2 | Viewed by 2640
Abstract
The aim of this article is to obtain a simple and efficient estimator of the index parameter of symmetric stable distribution that holds universally, i.e., over the entire range of the parameter. We appeal to directional statistics on the classical result on wrapping [...] Read more.
The aim of this article is to obtain a simple and efficient estimator of the index parameter of symmetric stable distribution that holds universally, i.e., over the entire range of the parameter. We appeal to directional statistics on the classical result on wrapping of a distribution in obtaining the wrapped stable family of distributions. The performance of the estimator obtained is better than the existing estimators in the literature in terms of both consistency and efficiency. The estimator is applied to model some real life financial datasets. A mixture of normal and Cauchy distributions is compared with the stable family of distributions when the estimate of the parameter α lies between 1 and 2. A similar approach can be adopted when α (or its estimate) belongs to (0.5,1). In this case, one may compare with a mixture of Laplace and Cauchy distributions. A new measure of goodness of fit is proposed for the above family of distributions. Full article
(This article belongs to the Special Issue Financial Statistics and Data Analytics)
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