Statistical Modeling of Skew-Normal Distributions

Statistical modeling of skew-normal distributions provides a versatile framework for capturing asymmetry in univariate and multivariate data. By introducing a shape parameter to the classical normal law, skew-normal families allow positive or negative skewness while retaining tractable likelihoods and moment expressions. In univariate settings, these models offer improved fit for data exhibiting departure from symmetry, as commonly encountered in finance, ecology and clinical measurements. Multivariate extensions further enrich covariance structures and directional skewness, facilitating more realistic characterisations of dependencies among variables. Applications range from robust risk assessment in asset returns to ecological inference on species morphometrics and from improved hypothesis testing in asymmetric residuals to dynamic filtering in state-space models. Modern advances focus on efficient inference via closed-form updates, expectation–maximisation algorithms and Bayesian computation, as well as information-theoretic measures such as Shannon and Rényi entropies to quantify distributional divergence. Together, these developments underline the global significance of skew-normal modeling in addressing real-world challenges where classical normality assumptions fail.

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Statistical Modeling of Skew-Normal Distributions publication trend

The graph below shows the total number of articles in statistical modeling of skew-normal distributions across all publications each year (not limited to Nature Index journals).

Technical terms

Skew-normal distribution: A generalisation of the normal law obtained by introducing a shape parameter that controls asymmetry while preserving tractable moment and density expressions.

Mixture model: A probabilistic model representing a population as a weighted combination of component distributions, each contributing to overall data heterogeneity.

Shannon entropy: An information-theoretic measure of uncertainty in a probability distribution, defined as the expected value of the negative logarithm of the density.

Rényi entropy: A one-parameter generalisation of Shannon entropy that emphasises tail behaviour and diversity of a distribution through a tunable order parameter.

Unified skew-normal (SUN) distribution: A flexible multivariate skew-normal family characterised by a unified stochastic representation that unites several skew and symmetric distributions under common parameters.

References

1. Bounds on Rényi and Shannon Entropies for Finite Mixtures of Multivariate Skew-Normal Distributions: Application to Swordfish (Xiphias gladius Linnaeus). Entropy (2016).
2. Modelling psychiatric measures using Skew-Normal distributions. European Psychiatry (2010).
3. A Bayesian Approach to Heavy-Tailed Finite Mixture Autoregressive Models. Symmetry (2020).
4. Some properties of the unified skew-normal distribution. Statistical Papers (2021).