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Constructing a multivariate distribution function with a vine copula: toward multivariate luminosity and mass functions
| العنوان: | Constructing a multivariate distribution function with a vine copula: toward multivariate luminosity and mass functions |
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| المؤلفون: | Takeuchi, Tsutomu T., Kono, Kai T. |
| سنة النشر: | 2020 |
| المجموعة: | Astrophysics |
| مصطلحات موضوعية: | Astrophysics - Astrophysics of Galaxies, Astrophysics - Instrumentation and Methods for Astrophysics |
| الوصف: | The need for a method to construct multidimensional distribution function is increasing recently, in the era of huge multiwavelength surveys. We have proposed a systematic method to build a bivariate luminosity or mass function of galaxies by using a copula. It allows us to construct a distribution function when only its marginal distributions are known, and we have to estimate the dependence structure from data. A typical example is the situation that we have univariate luminosity functions at some wavelengths for a survey, but the joint distribution is unknown. Main limitation of the copula method is that it is not easy to extend a joint function to higher dimensions ($d > 2$), except some special cases like multidimensional Gaussian. Even if we find such a multivariate analytic function in some fortunate case, it would often be inflexible and impractical. In this work, we show a systematic method to extend the copula method to unlimitedly higher dimensions by a vine copula. This is based on the pair-copula decomposition of a general multivariate distribution. We show how the vine copula construction is flexible and extendable. We also present an example of the construction of an stellar mass--atomic gas--molecular gas 3-dimensional mass function. We demonstrate the maximum likelihood estimation of the best functional form for this function, as well as a proper model selection via vine copula. Comment: 15 pages, 9 figures. Submitted to MNRAS on 7 May 2020, accepted for publication on 17 August 2020 |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1093/mnras/staa2558 |
| URL الوصول: | http://arxiv.org/abs/2006.05668 |
| رقم الانضمام: | edsarx.2006.05668 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1093/mnras/staa2558 |
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