A Constructive Representation of Univariate Skewed Distributions

We introduce a general perspective on the introduction of skewness into symmetric distributions. Through inverse probability integral transformations we provide a constructive representation of skewed distributions, where the skewing mechanism and the original symmetric distributions are specified s...

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Bibliographic Details
Published in:Journal of the American Statistical Association 2006-06, Vol.101 (474), p.823-829
Main Authors: Ferreira, José T. A. S, Steel, Mark F. J
Format: Article
Language:English
Subjects:
Applications
Arnold and groeneveld skewness measure
Bayesian analysis
Bayesian method
Bayesian regression model
Distribution theory
Exact sciences and technology
General topics
Integral transformations
Inverse probability integral transformation
Linear regression
Logistics
Mathematical moments
Mathematics
Methodology
Modality
Modeling
Probability
Probability and statistics
Probability theory and stochastic processes
Quantitative analysis
Regression analysis
Sciences and techniques of general use
Skewed distribution
Skewing mechanism
Statistical methods
Statistics
Steels
Tail behavior
Theory and Methods
Truncation
Weighting functions
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Summary:We introduce a general perspective on the introduction of skewness into symmetric distributions. Through inverse probability integral transformations we provide a constructive representation of skewed distributions, where the skewing mechanism and the original symmetric distributions are specified separately. We study the effects of the skewing mechanism on, e.g., modality, tail behavior and the amount of skewness generated. The representation is used to introduce novel classes of skewed distributions, where we induce certain prespecified characteristics through particular choices of the skewing mechanism. Finally, we use a Bayesian linear regression framework to compare the new classes with some existing distributions in the context of two empirical examples.
ISSN:0162-1459
1537-274X
DOI:10.1198/016214505000001212