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Bayesian Robustness in Change Point Analysis. JOURNAL OF STATISTICAL THEORY AND PRACTICE 2022. [DOI: 10.1007/s42519-022-00294-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Abstract
AbstractFor the family of multivariate probability distributions variously denoted as unified skew-normal, closed skew-normal and other names, a number of properties are already known, but many others are not, even some basic ones. The present contribution aims at filling some of the missing gaps. Specifically, the moments up to the fourth order are obtained, and from here the expressions of the Mardia’s measures of multivariate skewness and kurtosis. Other results concern the property of log-concavity of the distribution, closure with respect to conditioning on intervals, and a possible alternative parameterization.
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Confidence Distributions for Skew Normal Change-Point Model Based on Modified Information Criterion. JOURNAL OF STATISTICAL THEORY AND PRACTICE 2020. [DOI: 10.1007/s42519-020-00108-5] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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4
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Wang T, Tian W, Ning W. Likelihood ratio test change-point detection in the skew slash distribution. COMMUN STAT-SIMUL C 2020. [DOI: 10.1080/03610918.2020.1755869] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Tianping Wang
- School of Science, Xi’an University of Technology, Xi’an, China
| | - Weizhong Tian
- School of Science, Xi’an University of Technology, Xi’an, China
- Department of Mathematical Sciences, Eastern New Mexico University, Portales, New Mexico, USA
| | - Wei Ning
- Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Kentucky, USA
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A Selective Overview of Skew-Elliptical and Related Distributions and of Their Applications. Symmetry (Basel) 2020. [DOI: 10.3390/sym12010118] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
Within the context of flexible parametric families of distributions, much work has been dedicated in recent years to the theme of skew-symmetric distributions, or symmetry-modulated distributions, as we prefer to call them. The present contribution constitutes a review of this area, with special emphasis on multivariate skew-elliptical families, which represent the subset with more immediate impact on applications. After providing background information of the distribution theory aspects, we focus on the aspects more relevant for applied work. The exposition is targeted to non-specialists in this domain, although some general knowledge of probability and multivariate statistics is assumed. Given this aim, the mathematical profile is kept to the minimum required.
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Said KK, Ning W, Tian Y. Modified information criterion for testing changes in skew normal model. BRAZ J PROBAB STAT 2019. [DOI: 10.1214/17-bjps388] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Point Estimation of the Location Parameter of a Skew-Normal Distribution: Some Fixed Sample and Asymptotic Results. JOURNAL OF STATISTICAL THEORY AND PRACTICE 2019. [DOI: 10.1007/s42519-018-0033-4] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Vieira CC, Loschi RH, Duarte D. Nonparametric Mixtures Based on Skew-normal Distributions: An Application to Density Estimation. COMMUN STAT-THEOR M 2015. [DOI: 10.1080/03610926.2013.771745] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Hasan A, Ning W, Gupta AK. An Information-Based Approach to the Change-Point Problem of the Noncentral SkewtDistribution with Applications to Stock Market Data. Seq Anal 2014. [DOI: 10.1080/07474946.2014.961842] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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10
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Ngunkeng G, Ning W. Information Approach for the Change-Point Detection in the Skew Normal Distribution and Its Applications. Seq Anal 2014. [DOI: 10.1080/07474946.2014.961845] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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