2024-03-29T01:47:20Z
https://nagoya.repo.nii.ac.jp/oai
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2023-01-16T05:12:00Z
336:695:696
Constructing a multivariate distribution function with a vine copula: towards multivariate luminosity and mass functions
Takeuchi, Tsutomu T
Kono, Kai T
open access
[Monthly Notices of the Royal Astronomical Society, Volume 498, Issue 3, November 2020, Pages 4365–4378], [Constructing a multivariate distribution function with a vine copula: towards multivariate luminosity and mass functions] by [Tsutomu T Takeuchi, Kai T Kono], [2020], reproduced by permission of Oxford University Press [https://doi.org/10.1093/mnras/staa2558]
ISM: atoms
ISM: molecules
galaxies: evolution
galaxies: formation
galaxies: luminosity function
mass function
galaxies: star formation
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 a stellar mass–atomic gas–molecular gas three-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.
Oxford University Press
2021-09-07
2020-11
eng
journal article
VoR
http://hdl.handle.net/2237/0002001360
https://nagoya.repo.nii.ac.jp/records/2001360
https://doi.org/10.1093/mnras/staa2558
0035-8711
Monthly Notices of the Royal Astronomical Society
498
3
4365
4378
https://nagoya.repo.nii.ac.jp/record/2001360/files/staa2558.pdf
application/pdf
2.4 MB
2021-09-07