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• W3034423582 endingPage "4378" @default.
• W3034423582 startingPage "4365" @default.
• W3034423582 abstract "ABSTRACT 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 &gt; 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." @default.
• W3034423582 created "2020-06-19" @default.
• W3034423582 creator A5013964020 @default.
• W3034423582 creator A5068170634 @default.
• W3034423582 date "2020-08-22" @default.
• W3034423582 modified "2023-10-17" @default.
• W3034423582 title "Constructing a multivariate distribution function with a vine copula: towards multivariate luminosity and mass functions" @default.
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• W3034423582 doi "https://doi.org/10.1093/mnras/staa2558" @default.
• W3034423582 hasPublicationYear "2020" @default.
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