The mode-centric M-Gaussian distribution: A model for right skewed data

Scientific data are often nonnegative, right skewed and unimodal. For such data, the Mode-Centric M-Gaussian distribution is a basic model. It is R-symmetric and has mode as the centrality parameter. It is variously analogous enough to the Gaussian distribution to regard the Gaussian twin. In this p...

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Bibliographic Details
Published in:Statistics & probability letters 2015-12, Vol.107, p.1-10
Main Authors: Mudholkar, Govind S., Yu, Ziji, Awadalla, Saria S.
Format: Article
Language:English
Subjects:
G–M-G analogies
Harmonic variance
M-Gaussian distribution
Mode
R-symmetry
Right skewed distribution
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Summary:Scientific data are often nonnegative, right skewed and unimodal. For such data, the Mode-Centric M-Gaussian distribution is a basic model. It is R-symmetric and has mode as the centrality parameter. It is variously analogous enough to the Gaussian distribution to regard the Gaussian twin. In this paper, the essentials, namely the concept of R-symmetry, the M-Gaussian distribution, the roles of the mode and harmonic variance as, respectively, the centrality and dispersion parameters of the M-Gaussian distribution, are introduced. The pivotal role of the M-Gaussian family in the class of R-symmetric distributions and the estimation, testing, and characterization properties are discussed. The similarities between the Gaussian and the M-Gaussian distributions, namely the G–M-G analogies, are summarized. The work on the model, which is currently in progress, and the possible significance of the M-Gaussian in statistical applications such as regression analysis, Bayesian statistics and sequential analysis are outlined.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2015.07.016