The Linear Skew-t Distribution and Its Properties
The aim of this expository paper is to present the properties of the linear skew-t distribution, which is a specific example of a symmetry modulated-distribution. The skewing function remains the distribution function of Student’s t, but its argument is simpler than that used for the standard skew-t...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Stats |
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| Online Access: | https://www.mdpi.com/2571-905X/6/1/24 |
| _version_ | 1797608942239481856 |
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| author | C. J. Adcock |
| author_facet | C. J. Adcock |
| author_sort | C. J. Adcock |
| collection | DOAJ |
| description | The aim of this expository paper is to present the properties of the linear skew-t distribution, which is a specific example of a symmetry modulated-distribution. The skewing function remains the distribution function of Student’s t, but its argument is simpler than that used for the standard skew-t. The linear skew-t offers different insights, for example, different moments and tail behavior, and can be simpler to use for empirical work. It is shown that the distribution may be expressed as a hidden truncation model. The paper describes an extended version of the distribution that is analogous to the extended skew-t. For certain parameter values, the distribution is bimodal. The paper presents expressions for the moments of the distribution and shows that numerical integration methods are required. A multivariate version of the distribution is described. The bivariate version of the distribution may also be bimodal. The distribution is not closed under marginalization, and stochastic ordering is not satisfied. The properties of the distribution are illustrated with numerous examples of the density functions, table of moments and critical values. The results in this paper suggest that the linear skew-t may be useful for some applications, but that it should be used with care for methodological work. |
| first_indexed | 2024-03-11T05:54:44Z |
| format | Article |
| id | doaj.art-d0c1acec94ff4ab6b41b73d0c942bed7 |
| institution | Directory Open Access Journal |
| issn | 2571-905X |
| language | English |
| last_indexed | 2024-03-11T05:54:44Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Stats |
| spelling | doaj.art-d0c1acec94ff4ab6b41b73d0c942bed72023-11-17T13:54:03ZengMDPI AGStats2571-905X2023-02-016138141010.3390/stats6010024The Linear Skew-t Distribution and Its PropertiesC. J. Adcock0Sheffield University Management School, University of Sheffield, Sheffield S10 1FL, UKThe aim of this expository paper is to present the properties of the linear skew-t distribution, which is a specific example of a symmetry modulated-distribution. The skewing function remains the distribution function of Student’s t, but its argument is simpler than that used for the standard skew-t. The linear skew-t offers different insights, for example, different moments and tail behavior, and can be simpler to use for empirical work. It is shown that the distribution may be expressed as a hidden truncation model. The paper describes an extended version of the distribution that is analogous to the extended skew-t. For certain parameter values, the distribution is bimodal. The paper presents expressions for the moments of the distribution and shows that numerical integration methods are required. A multivariate version of the distribution is described. The bivariate version of the distribution may also be bimodal. The distribution is not closed under marginalization, and stochastic ordering is not satisfied. The properties of the distribution are illustrated with numerous examples of the density functions, table of moments and critical values. The results in this paper suggest that the linear skew-t may be useful for some applications, but that it should be used with care for methodological work.https://www.mdpi.com/2571-905X/6/1/24bimodalitycritical valuesmarginal distributionsmomentsskew-normal distributionskew-t distribution |
| spellingShingle | C. J. Adcock The Linear Skew-t Distribution and Its Properties Stats bimodality critical values marginal distributions moments skew-normal distribution skew-t distribution |
| title | The Linear Skew-t Distribution and Its Properties |
| title_full | The Linear Skew-t Distribution and Its Properties |
| title_fullStr | The Linear Skew-t Distribution and Its Properties |
| title_full_unstemmed | The Linear Skew-t Distribution and Its Properties |
| title_short | The Linear Skew-t Distribution and Its Properties |
| title_sort | linear skew t distribution and its properties |
| topic | bimodality critical values marginal distributions moments skew-normal distribution skew-t distribution |
| url | https://www.mdpi.com/2571-905X/6/1/24 |
| work_keys_str_mv | AT cjadcock thelinearskewtdistributionanditsproperties AT cjadcock linearskewtdistributionanditsproperties |