Uni- and multivariate extensions of the sinh-arcsinh normal distribution applied to distributional regression

Feng, Yuanhua; Härdle, Wolfgang

Uni- and multivariate extensions of the sinh-arcsinh normal distribution applied to distributional regression

No 142, Working Papers CIE from Paderborn University, CIE Center for International Economics

Abstract: This paper introduces first an extended SAN (sinh-arcsinh normal) family of distri- butions by allowing the transformed normal random variable to be unstandardized. A Log-SAN transformation for non-negative random variables and the associate Log-SAN family of distributions are then proposed. Properties of those distribu- tions are investigated. A maximum likelihood estimation procedure is proposed. A chain mixed multivariate extension of the SAN distributions and a corresponding distributional regression model are then defined. Those approaches can help us to discover possible spurious or hidden bimodal property of a multivariate distribution. The proposals are illustrated by different examples.

Keywords: Extended SAS distribution; Log-SAS distribution; MLE; chain mixed multivariate distribution; distributional regression; spurious and hidden bimodality (search for similar items in EconPapers)
JEL-codes: C14 C51 (search for similar items in EconPapers)
Pages: 32 pages
Date: 2021-05
New Economics Papers: this item is included in nep-ecm and nep-ore
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